Here is my breakdown genre by genre :
Fighting games = draw
Beat 'em ups = I'll actually give this one to the SNES. The MD has some elite ones, but the Capcom medieval themed ones + The Ninja Warriors Again put it over.
Sidescrolling platformers = draw. Lots of excellent stuff on both sides. SNES has the well known stuff and MD has the four Sonic games, Castle of Illusions, Kid Chameleon, Decap Attack, Dynamite Heady, and more minor hits like Ristar and Quackshot.
Sidescrolling adventure/hack'n slash = MD wins. The SNES has some excellent ones in Super Metroid, Valken, Actraiser, Mega Man series and Demon's Crest, but it's edged out by Rocket Knight Adventures, Strider, the 3 Shinobi games, Gunstar Heroes, Alien Soldier, Splatterhouse 2, Ranger-X, Alysia Dragoon, Chikki Chikki Boys, a couple of Monster World games (I'm excluding Contra, Castlevania and Ghouls 'n Ghosts from the discussion, as they have good iterations on both consoles).
RPGs = SNES wins, obviously. But despite having fewer of them, the MD actually has some elite ones in Phantasy Star IV, Shinning Force I & II and Landstalker
Shmups = MD wins
Arcade games = MD wins. this is a weird category since it englobes many genres. Excellent ports of Strider, Streets of Rage series, Ghouls 'n Gosts(superior version to the SNES one), Forgotten Realm, Gain Ground and many more(including classic Sega arcade stalwarts like Outrun, Space Harrier, Super Hang-On) put the MD over
Sports games = MD wins
Puzzle games = I have no idea, I don't know that genre at all!
'Sidescrolling platformers' maybe I could see it go for SNES. And 'arcade games'... hmm I guess a case could be made for a draw. But that's all I'm willing to change opinion on, the rest I'm hell bent on clamouring, so get used to it

Keep in mind I could have very well given the 'Beat 'em up' one to MD! with games like the Streets of Rage series, the Golden Axe series, Splatterhouse 3, and Comix Zone, amongst others