Black has the bishop pair (quite significant in an open position such as this) and after Kxf7 Nxe4 d5 has greater central control. Yes, he'll have some temporary problems with the position of the king, but this turns out to be nothing too serious. As any King's Gambiteer knows, you can sometimes afford to have your king wandering about a bit so long as you control the centre.
1.e4 e5 2.Nc3 Nf6 3.Bc4 Nxe4 4.Bxf7 is a similar line also generally thought to be quite alright for Black for similar reasons (most players go 4.Qh5 instead).
I was loking through the Opening Explorer randomly and found this:
http://www.chess.com/opening/eco/C47_Four_Knights_Game_Italian_Variation_Noa_Gambit
Apparently is a good idea for white: material is even and the black king is out of place. But, alas, statistics don't lie, and if you look at this opening stats, you can only conclude that it's a bad opening for white. Could someone explain me why, please?