Well, I'm not sure if I am representative of the other users here, nor have I been able to confirm getting to the Logitech webpage gives you the same menus on the TC30 as the 880, as others have claimed, I can however speak from my experience.
After a lot of trail and error I was able to log into the Harmony webpage with my TC30, but the menu items that so easily allow you to program favorite channels on the 880, are gone. Having just steup a harmony 880 for a friend, I know this menu is easily found, however when connecting my TC30 I couldn't find the same options. Ironically enough I did find a favorte DVD/CD menu for the TC, which I may have overlooked on the 880. I can't speak for the 720, but know the 880 offers the channel favorite and if it wasn't for the button lay-oput, would have turned my TC30 back in for an 880, but I dilike the buttons as they are to close together on the Harmony branded remotes.