Here's a pretty extensive "demo" of the Axe FX from about a year ago. I did this as a "resume" piece to get more work, but it works as a sampling of what the Axe can do as well.
One take, one guitar (until the "acoustic" sample at the very end) straight into the Axe straight into Logic, no outboard gear/FX/EQing/processing/etc used whatsoever. All changes made on the fly via the MFC just as I do in a live show.