The 360 interface looks a little more modern but is more effort to navigate (7 clicks to get to My Shows instead of 1) and is missing a lot of the features you get on TiVo (many of which are patented by TiVo, so wont be added later), off the top of my head a few of the missing features:
Undelete
Series Link manager (and the series link control is far more limited)
Skip back on fast-forward
Wishlists (setting up programs to auto-record based on specific actors, subjects etc.)
Setting up recording for programs that aren't currently in the upcoming TV guide
Radio channels (and therefore recording of radio)
Suggestions
Series Link+
Switching between the 6 available tuners
Ethernet control
There are probably a few other things I've forgotten
Also, if you have multiple boxes then on the 360 all recordings are pooled between them, you can't keep a separate pool of recordings on different boxes for different family members, which also means that if someone deletes a program on their box it is gone for everyone, and can't be recovered because there is no undelete option.