Why, do you have one?
I don't know much about the NES version but I used the SNES version. Being a consumer device, there's a lot of nonsense talked about PAR and GG by people who have no idea how they work. Of course, around here we know such things.
The main difference between the Game Genie and the Pro Action Replay, as far as I'm aware, is that the GG patches the ROM before the NES can see it, whereas the PAR patches the RAM while the system is running.
So to illustrate the difference, imagine you want infinite lives. The GG code will find a specified address in the ROM, perhaps the instruction for decrementing the lives counter, and replace it with something that does nothing, thereby giving you infinite lives. The PAR, on the other hand, will simply find the RAM address where the lives counter is stored, and freeze it.
The advantage of the latter is that you can use it to make your own cheats - I remember doing so on the SNES. Making Game Genie codes requires a good understanding of assembly. However, I somewhat prefer the GG approach, as a hacker, because it can be permanently applied to a ROM file if you so desire, and it just feels right. Also, there are some effects that can't be achieved by merely freezing RAM addresses.