Wow, I was wondering the exact same thing very recently. Here's what I've been told: Any code you can produce for a Game Genie can be duplicated on a PAR, but not vice versa. In other words, more codes are possible with a PAR. There are compatibility problems with some Game Genies and some SNES models (the mini and model 2); the PAR has no comptability problems. The Game Genie does not work as a convenient region bypass, but the PAR does.
Basically, PAR is better in every way possible except for availability. Also, there are three versions of the PAR. The third can hold 100 codes and comes with many built in.
Edited by - DeadAwake on 7/16/2005 5:05:53 PM