Palm Pros: Portability (play anywhere, anytime), fish exchange
Palm Cons: small screen, only 1 generation family tree, single player/game

PC Pros: Better graphics (fish looks better), bigger screen, multiple players/games
PC Cons: Can exchange fish, not portable (unless you carry a laptop all the time).

I've only tried the Palm version a short while, so others need to confirm, but I think the Palm version is more stingy. I played both on "easy" and the supplies on the Palm are much more expensive than on the PC, and you get less money for the fish on he Palm. This seems strange, as I would think the prices would be the same.

I too favor the PC version, but it's quite fun having your fish with you to care for at any time.