The following game is a good example of this dilemma for Black.
perrypawnpusher - NN
Giuoco Piano Thematic Tournament
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ke6 7.f4 Bd6
Black has two extra pieces. Why not give one back? How hard can the defense be?
8.d4 worked for White in Philidor 1792 - Guest839182, PlayChess.com, 2014, (1-0, 16), but I prefer the text.
8...Ke7 9. fxe5 Bc5
The Bishop is not having a good day.
11.c3 Ba5 12.Bg5+ Nf6 13.exf6+ gxf6 14.Qxf6+ Ke8 15.Qxh8+ Black resigned
Black will lose his Queen and be checkmated: 15...Kf7 16.0–0+ Kg6 17.Bxd8 a6 (or just about anything else) 18.Qg8+ Kh6 19.Qg5 checkmate