I had both growing up. At the time, it was easily the SNES. It wasn't even close. Games like Super Mario World, Street Fighter 2, Kirby, Legend of Zelda: Link to the Past, and Super Mario Kart kept me entertained. Games on the Sega Genesis didn't keep my interest for as long aside from the Sonic series.
With that said, looking back at the gaming library, I still prefer the SNES. However, a poster above made a good point that I agree with. Everyone knows the best SNES games and even the hidden gems since everyone around me grew up with a SNES. However, the Sega Genesis has a ton of games that are fantastic and hidden. If you ask most gamers about the SNES, their favorite games are the ones you always hear about, but the favorite games from a Genesis fan are more likely varied.
Looking back at things now, even with the varied games I love on the SNES, the Genesis has some games that I think are amazing, even better than SNES games. I personally think Phantasy Star 4 has aged so well that I like playing it more than any of the Final Fantasy or Square RPG's on the SNES. I enjoyed Super Mario World more than any Sonic game. I absolutely love the Streets of Rage series and Golden Axe series more than the Final Fight series. The most recent game I tried and absolutely loved, is Shinobi 3. I never tried it until this year and it floored me with its controls and gameplay.
All in all, both are fantastic. I don't prefer the SNES over the Genesis as I once did.