I agree, Pokemon Battle System is great. It is similiar to most FF games, however much more simple.
A pokemon can only have 4 attacks/moves at once (they can learn new ones, but have to forget an old move). Each has the special attributes (accuracy and power) and some fit to an elemental category as most pokemon themself do. Last ones also have some effects, e.g. the psychic ability 'synchronize' may add a status effect (poison, ..) to the enemy when being affected. Beside attack moves, some raise stats on the own pokemon (party) or lower them on the other side.
One great thing is, that you can play against an enemy on one screen (gamecube games). Usually this is a problem with those games, because you would see the move the other selectes, but since here it is simply done pressing one of the four D-Pad direction with no graphical menu as in the single player mode.
In the story mode, you, the trainer, can can also use items on one of your pocket monsters or echange them (you can carray up to 6 IIRC) and have a fourth game specific option.
In the GBA games matches are 1-1 and on the gamecube 2 pokemen battle on each site at once.
If it sounds interesting for you, I would recommend to rent a game (and probaly the console/handheld too) from a video store and do an evaluation yourself. But caution, it can be addicting.