7 Nb3 is better for the simple reason that in the English Attack you want to leave the f3 square free for the f-pawn to support an eventual g4 advance and a kingside pawn storm.
Najdorf 6.Be3 e5 7.Nf3 or Nb3

Nf3 if you're boring and unambitious. Nb3 if you want an exciting game. Nf5 if you want a worse game.

7.Nf3 is not unambitious at all. It's the positional approach focussing on the d5 square. It has been played by many strong GMs and the nice thing is that Black does not get his usual sharp counterplay which most Najdorf Players want - so with 7.Nf3 you can probably annoy them quite a bit.

I don't want to annoy my opponent, I want to checkmate them.
You are welcome to show us the forced mate in the 7.Nb3 line

There's no forced mate, but it's more fun to play for white and easier too. That's the whole point of the English attack...if I want to play positionally I'll play 6.Be2

Both are good. It depends on what kind of game you want.
With 7. Nf3 White castles on the kingside and has good control over the d5-square; Black will probably put pressure on the c-file.
With the more tactical 7. Nb3, White castles queenside and aims for a kingside attack; Black attacks on the queenside.
Either way, the best way to learn an opening is to learn the ideas of it. Some opening theory is needed, but mostly learn the ideas. Awhile ago a master played 7. Nf3 against me. I could see that he had the d5-square under control, but I had no idea what Black's counterplay was. In another game I had White and played 7. Nb3. A few moves later Black played a move I wasn't familiar with. I lost quickly, but if I had studied more games (not opening lines) I would have known how the correct way to respond was.

I have played 7.Nb3 a few times in correspondence games, and I'm not terribly satisfied with it. I wouldn't mind playing the knight to f3, but 6.Be3 Ng4! is extremely annoying ( I do not know any good way to prove that Black has overextended after 7.Bg5 h6 8.Bh4 g5 etc), so I have to play 6.f3 first, and then I cannot put that stupid horse there.

People that are intending the English attack can just play f3 before be3 to prevent the ng4 line right? That's what Caruana plays at least.

@ Airut: Both recaptures are OK. Taking with the pawn is less risky- and ambitious. Pretty much a matter of taste, and homework.
6.f3 e5 7.Nb3 almost always leads to a normal English attack, but Black may play 6...Qb6!? which is quite interesting. I have tried it once, and got a fairly nice position, alike the Botvinnik setup, but with some differences- like a knight on b6, which covers a potential d5 hole. White could probably have a slight opening advantage in a quite unbalanced position, but 17.Bd3?! certainly isn't the right way to get it.
Can somone who is knowledgable in both of these moves tell me a bit about them? They both seem like good moves with Nb3 being the more common and I'm trying to decide which one to play. I would like to know common themes that happen after playing Nf3 and Nb3 as well as any recommendations on which one to play. Thanks