IGN has made an excellent article detailing 10 main reasons to not get a Xbox 360 and instead to get the Revolution, which I have paraphrased here:

1-The Xbox 360 is ridiculously expensive, especially once you include all the accessories you require to fully take advantage of it.

2-The 360 has the same games that we've always had simply with prettier graphics.  PS3 will most likely have even better graphics while the Revolution will offer a totally new way to play games.

3-360 doesn't have Legend Of Zelda, nor any other Nintendo franchises, only Nintendo does.

4-Revolution is the most likely system for you to be able to play with your family, girlfriend, or grandpa with.  Playing a game of tennis with your gf vs. you playing halo and her watching.

5-360 doesn't have Metroid Prime 3, and it's important to note that Prime 3, Ubisoft's fps, and the new Final Fantasy on the Revolution are examples of games that will appeal to hardcore gamers.

6-Revolution will most likely be priced below 200 dollars.

7-Backward compatibility: Only on Revolution can you play Mario Bros from the NES, Super Mario World from the SNES, Mario 64 from the N64, Mario Sunshine from the GC, and Mario 128 from the Revolution.  360 cannot begin to compete with that.

8-Revolution is small, quiet and stylish.  The 360 is loud and clunky, and the power supply is roughly 1000 times the size of Earth.  IGN mentioned they had to turn up the volume of perfect dark zero just to drown out the sound of the 360 fan.

9-360 doesn't have Smash Bros. Online, nor does it have a free online service that allows for something as cool as a multiplayer Nintendo game; did somebody say Mario Kart Revolution Online?

10-The Revolution controller will change everything.  It will make the competition look dated and archaic.