But, i understand not wanting them to have their own devices. I would think it doesn't really matter what console you get if you're just looking for family games. Both are very similar, biggest difference seems to be some of the games that are console specific, but I don't think you'd really care about that.

We had a Kinect on our 360 and the kids used it for about a month before they got bored of it. Personally, I'd get whatever was cheaper, but I'm just a cheap Mormon.