You can just do both, though. Use interfaces for polymorphism, to define the interactions between your objects -- and then, if you want, use inheritance as one possible strategy for code reuse.
I guess it's a little strange that they haven't tried to put IE on the Xbox--but I'm glad they haven't. The whole reason I have a game console is to have an appliance that is dedicated to video games. I have plenty of other devices that provide a superior browsing experience.
I believe Live Mesh has an OS X client now. I tried it (on both OS X and Windows), and while it has most of same basic functionality as Dropbox, I found the interface off-putting.