I tried to think of every genesis equivalent to every well loved snes game. I did have a genesis as a kid and didn't have some of these imports growing up but after having played all of these games without the nostalgia as an adult it's pretty close to me.
Contra 3, Contra Hard Corps
Earthbound, Phantasy Star II/Shadowrun
F-Zero, Out-Run
Secret of Mana, Crusader of Centy
Super CV4, CV Bloodlines
Final Fantasy 2, Shining Force
Final Fantasy 3, Shining Force 2
Yoshi's Island, Rocket Knight Adventures
Final Fight, Streets of Rage
Turtles in Time, Streets of Rage 2
Final Fight 3, Bare Knuckle 3
DKC, Shinobi 2
DKC2, Shinobi 3
DKC3, Shadow Dancer
Star Fox, Panorama Cotton
Mega Man X, Pulse Man
Mega Man X2, Gunstar Heroes
Mega Man X3, Alien Soldier
Super Mario RPG, Landstalker
Kirby Superstar, Ristar
Kirby's Dreamland 3, Dynamite Headdy
Super Mario World, Sonic 3 & Knuckles
Chrono Trigger, Phantasy Star IV
Super Metroid, Monster World III/ Monster World IV
Super Mario Kart, Yu Yu Hakusho: Makyo Toitsusen
Link to The Past, Beyond the Oasis
Not all these games are that similar or even in the same genre but I do love every closest approximate on one console as much as the other. The only glaring weakness to me on the genesis side is racing due to Sega's best racers being in arcades at the time. I'll always slightly prefer genesis of course.
Edit: On second thought I might stack Comix Zone next to F-Zero despite their genre difference. Both banked a lot on their visual style and were pretty difficult games.