I have both. One collects dust (literally), one doesnt.
360 has a uva lot more games. Its not even close. On that fact alone, I would recommend a 360. Just be careful what games you buy for your kids. Unfortunately, if youre not a gamer, thats going to take some research.
I recommend this website
www.gamespot.com
There is a search bar at the top. Just type the game in your kid wants to play and read about it. You'll know if its age appropriate or not.
Otherwise though, my 360 just took a . I bought it at launch and the disc tray is scratching up my game discs now. I am too lazy to send it in (especially when theyre going to charge me $100 for repairing it... ing Microsoft).