We have a mini-ITX computer running onboard; it has an Atom dual-core 1.8GHz processor, 2GB RAM, a 4GB SSD, and power regulating and supply equipment to allow it to run on anywhere from 6-34vDC (this circuitry also powers the Kinect). We're all in love with it - it's small, around six inches square, and draws
maybe 30 watts and gets slightly warm while doing all its image processing.
Right now we're running into framerate issues while processing both feeds - getting only around 6fps from the Kinect and 12 at best from the other camera.. although I attribute this to the fact that we like our nice high resolutions too much - today we'll try moving down from 640x480 and we should see a huge gain in performance. Although the smaller the resolution from the Kinect, the less resolution our distance readings will have. Right now we have a reliable resolution of around 2-3 inches, which is acceptable.
I should also note that we're running the excellent RoboRealm software on the computer to do our vision processing - it's an amazingly powerful, GUI-based machine vision platform, and RoboRealm is giving free copies to any FIRST team who is interested (it's normally $50) - if nothing else, your team should grab a copy to play around with in the off-season.
I've found that it's a great tool for teaching the basics of machine vision, and its easy enough to learn the basics to get students who otherwise wouldn't step foot near C++ excited about programming and computers. I worked with two freshmen on our team to develop the Kinect targeting software, and both had no previous experience in programming. There is also plenty of room for the experienced programmer - RoboRealm has a full-featured API, built-in HTTP and FTP servers, and you can write custom image processing modules and plugins in C, Python, or Visual Basic. Check it out -
http://www.roborealm.com/