The AMIGA is vastly superior to the Atari ... It's able do show has a lot more colours on the screen, it has some special custom chips for graphics and sound (the "equivalent" of the PC graphics cards) that made a BIG difference between the competition.
I think there was some of the Atari games better than the AMIGA versions : about 2% of the Atari games :-D
If you get an A1200, you'll get best operative system I ever saw (it also crashes, but at least you dont' need to re-install it every 3 months

)
The Atari op. system was a piece of s....
Believe me, go for an AMIGA.
If you want a machine only AND really only for games, maybe the A500.
If you get a A1200, you'll get a faster machine and capable of serous work (just add it a hard drive and some more RAM and off you go)
Another important question is : how will you get the game disks ? From the Internet there are legal sites like backtoroots, but how will you tranfer them from a PC (with Internet connection) to your AMIGA without a hard disk ?
Maybe it's better to get a A1200 + hard disk ...