I don't think the Budapest is a bad opening, but it seems to me that in the Bf4 + Nbd2 line white can secure a safe risk-free += thanks to his bishop pair, without too many active possibilities for black.
Considering the Budapest

I played the Budapest for almost a year and my conclussion is that its difficult for black to create counter play if white knows the theory and how to take advantage after the opening.

I played it in a thematic tournament and found it to be quite fun, and I was able to take some of the ideas in other openings like the Chigorin Defense and 1. e4 d5 Nf3 nonsense line :)
As previously noted, I think 4. Bf4 is the hardest line to face, I recall watching a youtube from Seirawan about that line that he claims busts Black, so might be worth a look (though I'm sure there's alternatives Black could have played to avoid said 'bust')

The Budapest doesn't give any compensation since it isn't a gambit. (White can't safely keep the pawn.) However unlike most gambits, it seems blacks position is just passive.
A Budapest thread, well you knew I'd have to chime in.
I've played the Budapest Gambit since I started chess. Trappy and anti-positional? Well my impression is It really isn't any more trappy than any other opening (the Fajarowicz gambit with 3...Ne4 may be trappy but that's a completely different opening). In the Budapest proper with 3...Ng4 there's one famous smothered mate trap (called the Kieninger Trap) in the Rubenstein variation, and things can get very trappy if White plays 4.Qd4 to defend the pawn. And as for anti-positional, if anything it's a positional idea of establishing a strong knight on e5 that is one of the ideas of the opening, and if White ever plays f4 to kick the knight then the e-pawn can become weak, this tends to happen especially in the Adler variation. In the Rubenstein variation with Nc3 we have the positional idea of wrecking White's queenside pawns. Also in almost all variations Black gets a queenside pawn majority.
@PeskyGnat, Seirawan didn't cover 12...Re8 in that line and tended to just show outright mistakes by Black. 12...Re8 either prevents White from castling immediately or wins the pawn back. People can get in a lot of trouble here if they try to defend this pawn in the wrong way, for example 13.e3 h6 (threatens to the trap the bishop on f4) and if 14.Qg6 (which is the blitz move, stopping Black's threat and making a threat of their own) then Qe4 forces a favorable exchange of queens for Black and Black is clearly better. I don't believe Seirawan really thought the line he showed was a bust, it was an homage to Bobby Fischer's article and he was just trying to make an entertaining lecture and give people some ideas. This opening isn't busted at all.
@lolurspammed Black's position in the Budapest isn't passive, in fact, a position often arises in the Budapest that doesn't tend to happen in other openings, where both sides are castled kingside but don't have a knight on f6 or f3. This allows rook lifts along the sixth rank and also, it's easier for Black to get their pieces like the queen over into the "penalty area" with moves like Qh4. There are many different attacking ideas for Black in the Budapest not just the famous Drimer rook lift idea with a5 Ra6-h6, but many more and if you play and study the Budapest you'll start to discover them.
@FM Rumo75 Black is not obliged to give up the bishop pair in that line, in fact IM Timothy Taylor recommends not to in his book. Though I've tried both and I prefer to give up the bishop pair, after all it's a strong knight on e5. There's no reason why it should be worse than a bishop. Maybe it can be a pain for White too to always have to be trying to keep their bishop pair.
@Bishop_g5 what you showed is playing the opening incorrectly. The standard move is 6...Bxc3+ which tears White's queenside pawns to shreds and gives Black considerable counterplay. At least stick with an opening long enough to learn it past move 5 before you decide to give up on it.

Moskalenko, whom I respect, has a recent book on the Budapest. Silman reviews it favorably here:
http://dev.jeremysilman.com/shop/pc/Fabulous-Budapest-Gambit-The-p3565.htm
While top level GM versus GM encounters in the Budapest are still rare, at a minimum the opening is much better than previously thought.

Dolphin27 wrote : @Bishop_g5 what you showed is playing the opening incorrectly. The standard move is 6...Bxc3+ which tears White's queenside pawns to shreds and gives Black considerable counterplay. At least stick with an opening long enough to learn it past move 5 before you decide to give up on it.
I played the opening long enough to understand that 6...Bxc3+ gives nothing. I know that the Budapest is for romantic souls but i didn't knew that serves and illusionist like you. The double c pawns is not a weakness for white and black has absolutelly no plan to create considerable counterplay. Perhaps instead of wards you want to show something from your rich experience that everyone on this planet missed!?
I read Moskalenko's book and i don't see nowhere a concrete plan for black after 6...Bxc3+ or 7...Bxc3+. In order to sell the book more he didn't mention not even one from Gligoric games in the Budapest Rubinstein variation. Anti-selling example.

After 4...g5 black opens the kingside pawn structure with purpose to create a quick tactical strike on the Q side after recapture the e pawn and Bg7 but white's attack on the king side are more critical and faster because black does not have king safety!! White can leave the king in the center and survive, black can't and if he goes long castling, he suicide on the spot.

I would play the budapest or slav i a heart beat if I knew white would play 2. c4.
But the second I see 2. Bf4 I'm back to the dutch (or englund in bullet) for months. I don't want to play some silly system white plays exclusively. But when I venture 1... Nf6 I've had decent success with the budapest.
It's just like all opening -- you win some, you lose some, you draw some. You can play the absolute best lines ever, still get mated fast, or ground down with no counter play at all.

hi! Been playing this regularly nowand it seems to lead to equal positions (maybe a slight plus for white but at my level(1800-1900) I cant say white wins more than black. By the way Bxc3+ in the.position after 3.de Ng4 4.Bf4 Nc6 5.Nf3 Bb4+ 6.Nc3 is a must , since without it you just end a pawn down. 6.Bxc3+ 7.bc Qe7 8 Qd5 and now both 8...f6 and 8....Qa3 are interesting and approximately equal. I will give maybe some games when I'm on my laptop. In the more critical variation with 6.Nbd2 Qe7 7.e3 Taylor's line can be avoided but I wont give the line (it is not that hard to find)

hi! Been playing this regularly nowand it seems to lead to equal positions (maybe a slight plus for white but at my level(1800-1900) I cant say white wins more than black. By the way Bxc3+ in the.position after 3.de Ng4 4.Bf4 Nc6 5.Nf3 Bb4+ 6.Nc3 is a must , since without it you just end a pawn down. 6.Bxc3+ 7.bc Qe7 8 Qd5 and now both 8...f6 and 8....Qa3 are interesting and approximately equal. I will give maybe some games when I'm on my laptop. In the more critical variation with 6.Nbd2 Qe7 7.e3 Taylor's line can be avoided but I wont give the line (it is not that hard to find)

@ achja
I am sure Baadur who had Stockfish with him knew about it! The point is not who is in real danger with computer play but with human one and based on my optical view black seems much more exposed than white because his king side is much weaker. Now if you think that OTB you can find 12 or 15 straight on a row Stockfish moves you are fooling your self. Perhaps you should start to think with out your engine turn on! It's more useful.

Yeah I don't feel comfortable with ...g5 in the opening, even to shoo away a bishop. I had trouble with that in the past in some Nimzo-Indian lines.
Dolpin, by anti-positional I mean give up the e-pawn and accepting an inferior position statically, which can no longer solidly be placed on e6 and support a d5 strike, but the again white's d-pawn is gone now so it's one central pawn for another.
I think I'll stick with the QID/Nimzo complex and occasional Dutch. It seems like it gets harder to generate winning chances the higher you get. Which is natural since more skill means less likely to make mistakes and awareness of a system's flaws. I might consider the Slav too but the problem there is 3.cxd5 with a drawish position where it's difficult to generate imbalances.
The time to play for a draw is during an endgame where the opponent has all the winning chances, like a pawn ending where they decisively promote first so trying to promote one's pawn trying to win leads to a loss whereas stopping their pawn and allowing yours to be captured leads to a draw.
Or if your opponent is 200 or 300 points rated higher than you, and even then they'd still probably win since those numbers mean they're better than you. Then again upsets happen even at the world championship level (such as Kramnik and Deep Blue pulling upsets over Kasparov or Euwe vs. Alekhine) but the skill gaps there typically aren't as big.
@FM Rumo75 Black is not obliged to give up the bishop pair in that line, in fact IM Timothy Taylor recommends not to in his book. Though I've tried both and I prefer to give up the bishop pair, after all it's a strong knight on e5. There's no reason why it should be worse than a bishop. Maybe it can be a pain for White too to always have to be trying to keep their bishop pair.
Regarding the option of black keeping the bishop, I wasn't aware of that. Always thought Bd6 were inferior for some reason, suppose I should take another look at it.
The Ne5 is a well-placed piece for the moment, but that doesn't make it as good as a bishop. White's advantage isn't large, but it's stable, having a few pawn-breaks at his disposal and usually the better endgame.

If you read Timothy Taylor's book carefully, you'll find that there are plenty of good reasons not to take up the Budapest. White has several ways to gain an edge, and at least one of those is a main line. Taylor had no answer for it in his book. Thankfully, he was honest enough to point it out to his readers.

Personally, I'd be happy never to play against the Budapest again. I've beaten strong players as White, but I've also lost to some cute trappy play, especially in blitz time controls. It's a very tricky opening that should favor white with best play. Unfortunately, in correspondence, that edge may not be quite enough to win though.
So, if you like trappy play that should lead to a clearly inferior but not lost position, the Budapest may be for you.
I played the opening long enough to understand that 6...Bxc3+ gives nothing. I know that the Budapest is for romantic souls but i didn't knew that serves and illusionist like you. The double c pawns is not a weakness for white and black has absolutelly no plan to create considerable counterplay. Perhaps instead of wards you want to show something from your rich experience that everyone on this planet missed!?
I read Moskalenko's book and i don't see nowhere a concrete plan for black after 6...Bxc3+ or 7...Bxc3+. In order to sell the book more he didn't mention not even one from Gligoric games in the Budapest Rubinstein variation. Anti-selling example.
Doubled isolated c-pawns and an isolated a-pawn aren't weakness for White? Um, ok. I suppose the correct way is to take on c3 without wrecking White's pawns as you showed in your diagram, that makes perfect sense.
BxNc3+ is a very basic and key move for Black in that line. If you don't grasp why that move is good you have no business even studying openings, you need to go read "Basic Strategy for Beginners" before you run your mouth off about anything, much less an opening you don't even play. (Oh but you used to play it, and gave up on it before you learned it past move 5, I know this makes you an expert about it.)
And apparently you didn't read Moskalenko's book as you claim (or else you have zero reading comprehension) because he shows lots of ideas, in particular, the Schlechter Knight manuever of Nf6 to e4 to c5 blockading the isolated doubled pawns. This is elementary strategy straight out of My System. Meanwhile White's queen is exposed in the center, Black has a lead in development, semi-open e and f files, and the knight on c6 can hop to e5 creating what Taylor referred to in his book as "Schlechter's double-fisted knight blockade", all this ON TOP of the shattered White queenside and weaknesses to work with adds up to considerable counterplay. This is the price White pays for keeping the extra pawn and why lots of players prefer Nbd2.
If you read Timothy Taylor's book carefully, you'll find that there are plenty of good reasons not to take up the Budapest. White has several ways to gain an edge, and at least one of those is a main line. Taylor had no answer for it in his book. Thankfully, he was honest enough to point it out to his readers.
I have read Taylor's book carefully and tested out his different ideas in my games. Some of his ideas I've enjoyed, others, like his recommendations to avoid the Adler variation with 4...Nc6 and to go to great lengths to avoid giving up the bishop pair in the Rubenstein variation with Nbd2 I've not had great luck with.
In particular his suggestion to avoid the Adler variation just seemed like he didn't want to go to the effort of writing a chapter about it. HIs given reasoning for avoiding the Adler variation is twofold. First he claims the Drimer rook lift plan of a5-Ra6-Rh6 is hard to enact because White will be able to block the sixth rank, but why does Black have to do that rook lift? There are many other ideas for Black, and if he wants to do a rook lift at some point, why not just Re8-e6? His other reason is that White's plan with an early f4 is strong. I've not seen this, all Black has to know is a few basic ideas, such as blockading with f5, and then White just has a weak e-pawn. Just as the Drimer rook lift plan isn't much to worry about if White knows about it, niether is the f4 plan.

I won't go into detail since his discussion of the line is probably the most valuable part of Taylor's book. But his analysis of the various "f4" games in a certain line has the pedigree of World Champions and gives White a really nice edge. I've won a few cc games using his recommendation in his book designed for Black!
I've always been turned off by this opening because it initially came across as trappy, anti-positional play. However, after reading Soviet Middlegame Technique, Questions of Modern Chess Theory (which covers some advanced opening principles that seem to violate basics but really don't on a deeper level), and studying dynamics in general I appreciate the piece activity as compensation.
I won't mainly play it but it seems like a decent attempt at playing for the win. Sure Kramnik probably can't be beat if used against him but I'm not playing against him. I'm also still studying the Dutch (Leningrad and sidelines) and Queen and Nimzo Indians but otherwise feel secure in my theoretical knowledge on those fronts.