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I would probably be tempted to go for the Wii over the XBox 360 sheerly because of the uniqueness but that is a personal choice.
The XBox is much more of a solid, 'traditional' console and a lot of great games are being or already have been developed for it.
The Wii isn't so much of a technical machine and the graphics aren't truly next-gen but there are quite a few really innovative things going on with that console and it will probably only get better as more developers release new games for it. |