Very different openings. Depends on your style which is "better."
I like the Dutch (classical, not leningrad) because it imbalances the game, and gets out of those closed symetrical games that 1. d5 gets you.
I've tried the KID, and know that it has a great reputation, I can't figure out how to play it without getting rolled though,
It just depends on your style (As any other opening) and tourney standings as well. The KID is pretty popular while (Relatively) few dare to venture the Dutch. If I knew how to play the (Leningrad) Dutch effectively, I would probably use it over the KID. It is pretty difficult to play though.
Btw, a d4 player that has at least 'some' idea of the Dutch would play 2. g3 and delay c4 until after they castle. (Unless they are playing the exchange sac/ h4-h5 line)
lol, I know that h4 for white isn't supposed to win, but doesn't black's king just look so horribly vulnerable to h4 in the second position? He's down in space, AND his king is loose. Does anyone know the theory on that? So if you're going to play the dutch as black you should be prepared for many aggressive white tries that can be tough to weather with no preparation. I'm guessing black has to find a very concrete defense to this plan.
The dutch IS a relatively sound (though not thought to be quite as good as more mainstream defenses but it is used by gms) way to create an imbalance, but by weakening the kingside he's also commiting to some positional weaknesses (and white can try to exploit them both tactically and positionally), and in some lines he's down in space. As black you need to know when to play dynamically and sometimes you have to find creative solutions to counter white plans. For these reasons the dutch is a difficult and exhausting opening to play from the black side, but if it can be mastered you get a lot of counterplay and dynamic chances you wouldn't get if you played a more common opening. But there is a price.
The KID gives black a much more solid position, though down in space, and white has committed three of his pawns to the 4th rank, creating potential weakness, so when black strikes at them, usually with ...e5, he either gets white to play d5 (when the closed center lets him attack on the k side, then it gets sharp), or if white can keep the tension in the center black may have to capture on d4 and focus on white's weak dark squares and put pressure on the position that way. Unless like the 4 pawns attack is played (a critical line to know for black) black should be able to eventually equalize space in the center, when there is usually a nice imbalanced middlegame to be played.
To me (just at a glance) it looks justified, actually. White's even ahead in space, and the g6 pawn is such a clear target.
Elubas, you mentioned the four pawn opening. How does black counter this?
Theese are more powerful attack from White on KID and more powerful attack from black on dutch.
Conzipe this may seem so slow, but how does ...Na6 prepare ...e5? To get ready to jump into c5 or something?
So yeah, the benoni idea ...c5 (note that this transposes into an f4 benoni, BUT with the huge difference of avoiding lines where white plays Bb5+ to disrupt black's development.) it's what's recomended in my book and is a pretty fun, sound way to play, but ...Na6!? is also interesting.
However GMs doesn´t play them, I like the Dutch defense above the KID, and not because I´m Dutch. 
I think the f5-pawn does a great job there, and helps with defending the kingside AND attack whites one!
I think the Dutch and KID compared is comparing a steel,not very sharp dagger(KID) to a sharp magical dagger striking both you and your opponent.
The KID could get more different
I think the Dutch and KID compared is comparing a steel,not very sharp dagger(KID) to a sharp magical dagger striking both you and your opponent.
The KID could get more different
26. Qxe6+?? Nxe6.
lol
And thanks conzipe. Very fascinating.
Which is better, and why?
KID
Dutch