Basically it has to do with the fact that the Evans is a gambit. In the Hungarian Defence White can build up his position and place a great deal of pressure on Black and win in the late middle and endgame. The Evans does not have this luxury, white is after all a pawn down and if it comes down to an endgame, white will lose.
Evans Gambit Be7
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I played recently Be7 in OTB Evans gambit game against 200 higher rated player and drew.
I'm not sure if this is the correct reason, but personally I like Be7 because it allows black to keep the extra pawn, while maintaining the ability to castle.
If 5... Ba5, for instance, then 6. d4 d6 7. dxe5 dxe5 8. QxQ ... now black must either recapture with the knight (giving up the e pawn) or with the king (giving up the option to castle).
On the other hand, if 5... Be7, then 6. d4 d6 7. dxe5 dxe5 8. QxQ ... now black can recapture with the e7 bishop, maintaining the option to castle while holding on to the e pawn.
I rarely play 1... e5 these days, so I don't encounter the Evan's that much. Maybe someone else can confirm what I've said and see if it's right...
I play the Evan's Gambit sometimes and have had difficulty against 5....Be7. It's a good solid move (a pawn up). Here's a game I unjustly won against willing opposition..... my opponent (2090 when the game started) mass resigned some games and I was one of the recipients. I'm clearly worse in the final position, and yet felt that I'd played okay. Please feel free to improve on White's play.
http://www.chess.com/echess/game.html?id=11997561
Firstly, you seem to imply that the Hungarian Defence is bad. It isn't, it's just very solid and not immediately active, but that's not a bad thing. It's a matter of style. If it has been played by two post-war World Champions (Petrosian and Smyslov), it can't be bad.
Secondly, is the Be7 variation really considered best in the Evans? I thought it was just one of the options, besides Ba5 and Bc5, with Ba5 being the most popular.
I've read an article on wikipedia about the Hungarian Defence. (e4 e5 - Nf3 Nc6 - Bc4 Be7). But Black has a cramped position and white has a strong development. Why is Be7 the best move for Black after c3 at the Evans Gambit? Black has the same cramped position.....