Initially I like White's position, as he will castle very soon and is 1 pawn ahead; whereas Black must get his KB out first.
If Black re-establishes material equality with ...Bxd5 then a variation can be, 1 Bxd5, Nxd5 2 0-0, Nxe3 3 Qe2 and Black looks fine.
the first thing that comes to mind is Rxa2 but I will have to check, Black does somewhat lag in development, ah, not good after 0-0 from White
Black is worse here. According to Stockfish it is +0.5 to +0.7 and evaluation is quite stable.To me it seems that you will end up in an endgame with bishop and pawn against a rook, e.g. after 1...Nxa2 2.Bxa2 Rxa2 3.O-O Qxd5 4.Re1 Qxd1 5.Rcxd1 Ra6 6.Bf4+ Re6 7.Ng5 Be7 8.Nxe6 fxe6 difficult to say if that is enough to hold.
After 1... Bxd5 2.0-0 black is clearly worse.
One reason your engine swings might be that you setup the position without specifying castling rights?
Btw, the posted position has the black king on d1.
My engine swings pretty wildly in its evaluation of this position, which I can expect to reach in some games. Im hoping someone experienced in analysis can tell me:
1) What the best continuation is for black and its evaluation.
2) How difficult they feel it would be to survive in classical time controls.
(Black to move)