You decide:
PS2.... a "slightly" younger group of players. Way more games of all varieties, works as a stand alone DVD player, has oline play available. I'm 42 and still play PS2.
XBOX -- Way LESS games, Better graphics, geared to a slightly older crowd. Better at online play than PS2. To be a DVD player you need to buy a remote control. I'm 42 and still play XBOX.
I'm 42 and I own, but rarely use, a Nintendo Gamecube.
BTW, in the next year, both systems will be on their way out the door as the "next generation" of each system becomes available.
From what I gather, and this is NOT CONFIRMED, the PS3 will play PS2 games, while the XBOX is not planned to be backwards compatible.
These current systems are a geat value for the money. The new systems, with a lot of new features, are expected to be at least $300, and possibly as much as $500 when they get released.
EDIT: BTW, in rereading your post, for a 6 year old I would get a Nintendo Gamecube! And if he or she has a GAMEBOY, there is an adapter for the GAMECUBE that allows them to play GAMEBOY titles on it, and see them on a TV screen.