I love the Giuoco, but I hate this line. I hate c3, I usually just follow up with d3 after 3...Bc5.
Giuoco Piano - Am I missing Something?
The Moller Attack is an interesting line, however with the Black's position having some latent potential I think the Black should be able to hold a pawn advantage, or at worst consolidate with equal material. That horribly misplaced Black Knight is actually flexible and can usefully redeploy to g6 or f5, etc.
13.Qxd6, as played in most games from this position, seems to be reliable for White. 13.Bg5 d5, as you said, is a bit more murky, although White has compensation for the pawn following a sequence like 14.Bxd5 Nxd5 15.Qxd5 Bxg5 16.Nxg5 with possible Nh3-f4 and play against the isolated d-pawn.
All good comments. cbgirardo, what I'm seeing is continuation of 13. Bg5 d5 14. Bxd5 Nxd5 15. Qxd5 then 15. ... d6. I'm having trouble justifying the sacrificed material at this point at Black develops the other Bishop and Rook, much less seeing it as "White stands slightly better" as indicated in ECO.
I quit playing Giocco because of this exact line, and I think the book is wrong. Black is better here. My advice (which admittedly is not worth much) is to do what most other serious players eventually do with this opening...... dump it for the Ruy Lopez which gives you the same kind of play with more solid advantageous lines for white.
Sorry I know this is not what you wanted to here.
ECO lists this position as "White stands slightly better". C54 note 19. The continuation shows 13. Bg5 Ng6, 14. Qd5 where "White stands slightly better". In all of my research I can't find a refutation for 13. ... d5 (following 13. Bg5) where all lines seem to lead to "Black has the upper hand". Am I missing something? All lines I've explored for White seem to fizzle under careful play by Black. Help!?!?