Basically any internal PCI/PCI Express capture card would be fine. Avermedia has several that will work perfectly well for XBox.
Probably the best capture card, and the one I usually recommend these days is the XCapture-1. You have to have an Intel or Renesas USB 3.0 port in order to use it, and it's kind of pricey, but it's probably the best consumer level capture card out there. It's also probably overkill for what a lot of people use capture cards for, but it's just such a nice piece of hardware...