Well I was a proud Genesis owner back in the day, but my comparison here is a lot closer than I thought. Honestly, I can't really come up with a winner. They are very different games.
Here are two screens I took of the first two levels:
They have very different visual styles. The SNES has some really nice backgrounds, and overall I feel it has a nice vibe to it. A little different colors. It's also probably missing some of that pizzazz on the animations like the guards dropping their pants and the camels spitting out things. I mean the first image you see booting up the Genesis is the genie shooting down a bird on the logo screen lol. SNES doesn't have much of that and comes off as pretty rote and routine, but with good jumping mechanics.
The SNES definitely has tighter platforming, and you can tell it's a much more smooth game in that right. Sega has a more Aladdin centered perspective with sword fighting and apple throwing everywhere, and Abu shows up in the bonus levels as opposed to following you along your journey on SNES. His Sega bonus levels have some rad synth music. Music is whatever overall, but you can't deny the charm and originality of the Sega version. I mean, they are both pretty good. Very characteristic of the systems. The Genesis is definitely a little more unique with flair like the movie, and the SNES version is a bit more classic. I think I prefer the Sega version here folks.
Obviously, I just played the original level 1 in each game. I think I'm honestly gonna go through both of them. I really love Aladdin and this is hitting some nostalgia vibes hard. I know a couple levels are pretty crazy as you get further into the game on the Sega system, and I actually never played the SNES version.
So there you go. Both fabulous games if you ask me.