You're taking a calculated risk buying pre-owned. The difference between refurbished and "used" is that the refurb unit has already had at least one component fail. While it is true that the failed component has been fixed/replaced, every other component in the unit is still used and thus has a shortened time before failure.
That being said, new console failure rates are high enough (when compared to used) and pre-owned prices low enough (when compared to new) that the risk is probably worth it. They're not designed to last for 10 years so even if you buy brand new, you probably won't get THAT much more life out of it.
On the 2nd question, how many kids do you have and how old are they?
The 360 has Kinect, which is great of kid games, but if your kids have outgrown the Wii, I'm not sure the Kinect will be a huge attraction for them. There's also the fact that if they want to play online, each one of them will have to have a Gold account, so if you have 3 or 4 kids, that could be a lot of extra money.
The biggest differentiator for the XBox is probably Live Arcade. There are hundreds of downloadable games on the XBox that aren't "hardcore" or "Blockbusters" but they're not "kiddie" either. There's a ton of fun games on Live Arcade.