These could not be any more different
the 770s are bottom heavy with a dip in the mid and a bright top end. for bass heavy music I find them a blast, they seem to enhance the bottom and the top a lot.. which is enjoyable for hard rock IMO.
the 880s are much smoother and while they have a good bottom end its nothing compared to the 770s. They also have a much more even midrange, and I dont find the top end as bright as the 770s, but rather smoother.
I enjoy them both, just very different cans. I like the 770s with a Predator on mid gain, for Linkin Park, Pillar, Nickelback etc, and the 880s with the Predator on high gain, for smooth jazz, and new age music. They can handle rock just fine, I just like the fun factor of the 770s when I want to hop on the volume a bit for something harder.
I have been an AKG,Grado and Senn fan for years... I was introduced to Beyer this year, and have been really impressed thus far, they make really nice stuff, expecially for the price.