I looked at the 770's & 880's before deciding I liked the DR-3 better, and on top of that, it was way cheaper. I based my decision on playing around with them at the music store.
While I haven't been overly enamored with the preprogrammed patterns on the DR-3, the thing is totally user programmable...I've programmed my own patterns. You can also define drum kits, combine patterns into songs and stuff like that. each "patch" can have 6 different drum patterns (8 including intro and ending), in addition to 3 different fill patterns. The patterns are triggered from the buttons. Additionally, these patches can be programmed into complete songs.
The dr-3 also has bass built-in as well.
The menus can be a little awkward, but if you're patient, it'll do a lot.
One thing the dr-3 can't do is write out - it's got a MIDI in but not an out...so there's no way to create a program to save patterns. I don't know if the 880 or 770 has that capability. Something to consider.