There are some really violent and offensive games for the XBox and the XBox 360. There are also some very family friendly games. We have all the consoles and probably play the 360 the most. (Well, until the last couple of weeks - right now we're playing lots of Little Big Planet on the PS3 and Animal Crossing on the Wii).
Do you mean XBox or XBox 360? If you are looking at buying a new one, that would be the 360. Off the top of my head, some family friendly games for the 360 are:
Lego Batman, Lego Indiana Jones, Lego Star Wars, Beautiful Katamari, Viva Pinata, PGR4, Madden, Burnout Paradise (though you do crash cars, but no one gets hurt). . . I'm sure there are lots of others, as well. We play Rock Band and Rock Band 2 often as a family, but some of the lyrics might not be great for every family.
My son is 12 and has been playing the XBox and the XBox 360 for several years, but of course we don't allow him to play the more adult/offensive games. Has your son mentioned specific games he is wanting to play? If he wants the console for Grand Theft Auto and games like that then I can see why you object. If he wants it for the more family friendly games, then you could get it and the games you approve of and just not get the games you object to.
Anyway, I guess my point is, there are family friendly games available now for all the game consoles, and there are objectionable games for all of them, too. (Even the Wii! Resident Evil, for example.) Just because the console can play games like Grand Theft Auto doesn't mean you have to buy the game, so just getting the console doesn't mean your child will be playing all the offensive games - but it does mean you'd have to be willing to research games before buying them. If you have any specific questions I'd be happy to try to answer them, and I know there are lots of other gamers on here who will probably weigh in. Good luck!