I think it wins in platformers, though just barely.
Sonic 1-3+K, Ristar and Rocket Knight Adventures
vs
Super Mario World 1 and 2, DKC 1 and 2, and Do-Re-Mi Fantasy
I'll take the first set.
Beat em ups are easy win for the Genesis: Streets of Rage 2 and 3 vs an iffy Final Fight port and two mediocre Final Fight sequels.
Spaceship shooters are another easy Genesis win. Too many to name on the Genesis, vs basically Gradius III and UN Squadron on the SNES.