Games based on licensed tv or movie properties are often terrible. Disney games are usually an exception to that rule and Aladdin is a great example. While Aladdin was released for both the Super Nintendo and Sega Genesis, they were different games developed by different companies.
Aladdin became one of the best selling games on the Sega Genesis coming in at number three overall. It is a side-scrolling platform game and the levels generally follow the plot of the movie and culminates in a confrontation with Jafar in his palace. The game was released in late 1993 and featured some of the best graphics and animation on a 16-bit system at that time.
The Sega Genesis version of the game was the source for the Amiga and DOS ports. If you want to play the Sega Genesis version of Aladdin or any other, then you will have to track down an original copy or risk the wrath of the Disney police and use emulation.
Images above are from the Genesis version of the game.