It's fishy ... Levenfishy Dragonfly variation.
The Levenfish Dragon

Stick to the Yugoslav, and you need to completely change your mental attitude.
The way to get better is to play what you know and what is sound, NOT play what your opponent doesn't know or unsound garbage just to try to pull of some form of trickery!
The Levenfish is actually a weak line and it's White that's fighting for a draw if Black does know what to do against it. For starters, 6...Nc6 or 6...Nbd7 is safer than 6...Bg7.
Think of it like this. Let's say you play some trick line against a player that is no good if he knows how to defend it. You happen to win. Can you use it against him the next time you get White versus him? NO! He'll know what to do by then through research. If you play a main line system, like let's say you beat his Caro-Kann with the Advance Variation, can you throw the Advance Caro-Kann at him again the next time you get White against him and expect to have any shot at winning against him again? ABSOLUTLELY!
Now if you have an opponent you have played many times, and you want to throw him off with another item that is sound, like in my case, I have absolutely no problems playing the French, Caro-Kann, or Petroff against anybody. Last 4 times I faced a certain player, I played the French every time. There is absolutely no problem with throwing the Caro-Kann or Petroff at him, but don't do something stupid like say, 1.e4 e6 2.d4 d5 3.Nc3 c5?, a line known to be bad, just because you think he might not know what to do against it because nobody plays it. Turns out, it's not that terribly hard to figure out why it's bad, whereas the Caro-Kann and Petroff are legitimate defenses!
It's just like trying to set a trap in the position. Let's say you have a specific plan in mind, and it involves a Knight move and Bishop move as your next two moves, and if you move the Knight first, you get this position after your Bishop move on the next move, and if you move the Bishop first, and the Knight the following move, you have the same possibility, but by moving the Bishop first, you happen to set up a possible trap. In this case, setting up the trap is fine as it makes no difference otherwise if he doesn't fall for it. However, in a scenario where you think you have a cool trap if he misses it, but if he doesn't miss it, the move is useless and you have nothing better than to go back to where you came from, then the idea is idiotic to play the trap. Play a more productive move.
Same concept here. If you have another sound opening you happen to know, like 1.d4, or the English, in your case, rather than 1.e4, then by all means do it. But don't play garbage like the Levenfish just to deviate.

I see why some players might prescribe it. Opposite sides castling games are typically just a matter of calculation and calculating pawn storms and memorizing ridiculous tactical lines and such. But the same side castling lines lead to even games and the players don't have simple attacking lines to memorize or anything.
I don't really know the big difference between 6.f4 and 6.Be2. Maybe it's just tactics or something. But this was a game I saw in the dragon that made me, at one point, decide to play sicilian positions with same side castling:
http://www.tim-thompson.com/gaprindashvili.html

As white I commonly play against lines like the dragon, the yugoslav attack has been recommended to me by high ranking players but I feel like every dragon player understands how not to lose as it is all they play against. I recently tried out the Levenfish dragon and found that many players struggle in the position from a lack of knowledge is it worth continuing with it or should I stick to the Yugoslav.
If I were you I'd only play the levenfish in bullet. Most dragon players know how to counter it. It's a theoretically inferior opening. The reason why I say bullet is that most people premove a lot, and after Nf6 Nc3 g6 f4 most people will have premoved Bg7 and that's winning for white. But if I were you I wouldn't play it in any other time control other than bullet.
As white I commonly play against lines like the dragon, the yugoslav attack has been recommended to me by high ranking players but I feel like every dragon player understands how not to lose as it is all they play against. I recently tried out the Levenfish dragon and found that many players struggle in the position from a lack of knowledge is it worth continuing with it or should I stick to the Yugoslav.