Both platforms have advantages and disadvantages, but after having both I find the X-box wins out. There's a lot of non-violent games to choose from, and more are always being made. One thing I like about the X-box is that is doubles as a cd and dvd player (when you get the 'DVD remote' usually sold seperately), so it can clear some space on the entertainment center's shelves by doing the work of three components. I tend to use mine more for movies than gaming lately...
I'd recommend checking Costco (or the like) for a bundled package deal on the x-box. That's how I got mine and in the bundle came with the DVD remote, extra controller, memory card and two games for under $200. Not a bad way to go when you add all that individually.
I'd stay away from the new x-box 360 for now...the "i gotta have it" new toy prices almost always drop nearly in half if you can wait a year or two, and the old one would more than likely suffice for your childrens needs currently. (plus if it gets broken you won't be out top dollar...)
If you do go the x-box route then you have to get Forza Motorsport for yourself: it's got Laguna Seca, Road America, Road Atlanta, to name a few of the real tracks...but most importantly: it's got the entire Nurburgring Nordschleife!! (and about 200 cars, old and new, to choose from...no 2002's unfortunately...)
Good luck...happy gaming.

_________________
Shad
'70 2002 "Bimmerschmitt"
'70 2002 BADUDA aka 'Wall Art'
'72 2002 25HR Thunderhill Enduro Legend (of the mind)
'73 2002 Rolling Shell = Future Money Waster
'79 528i New Daily Driver