What are you making? Its worth paying for a full feature if its a serious production.
I Made a short film a few years ago.. makes a big difference having the right software than a low quality cheap product.. unless its nothing serious. Same goes for recording live with camera
For an XBox plug it into your video recorder/DVD recorder/HDD recorder/w.e and set it to aux input and press record.
Or, plug it into your TV-in card on your computer and use fraps.