Petroff: 4. Nxf7!?, Kxf7 5. Bc4+

What response is better? I have posted some lines. After d5, Bxd5 I'm not so sure that black is better. Must be something better than d5., I have won some games thanks to the queen's trap, but I need something tougher.

Now you have a massive advantage (as black) ... just play :P.

Well, your material advantage is obvious, the only thing you have to try now is to develop some minor pieces and get you King safe. I doubt that Bc4 is the right move for white here actually. It's easily met by Be6 isn't it? As far as i know White should proceed with d4, complete his development quickly and try to take advantage of his initiative and actieve pieces.

1...Be6 looks stonger than 1...d5

If white trades, black is better as it takes white alot of time to start an attack.

If white plays 2.Qe2, black plays 2...d5, when it doesn't lose a pawn.

Your opponent was incorrect he should have played 5.d4! but Nc3 is good too.

This is too optimistic. The Cochrane Gambit, in the right hands, can be *very* dangerous. The consensus seems to be that, after 5 d4, that black has an advantage, but has to play very carefully for quite some time before it can be exploited properly.

After 5 Bc4, 5...d5 is the theory move. White misses his opportunity to create a mobile pawn "phalanx" in the center, and with it tosses most of his advantage.

After 1 e4 e5  2 Nf3 Nf6  3 Ne5 d6  4 Nf7 Kf7, the move 5 Bc4 is one of those rare cases in which the most "obvious" move (it develops a piece with check) isn't the best move.  Current theory advocates 5 d4, as others have noted in this thread.