I've got a 710. Was my first deer rifle (and only one so far) and I've had no problems with it. Shoots great also. I was in the Bass Pro Outdoor World in Nashville a couple of weeks ago and they had a 770 out on one of the racks. The biggest improvement is that the bolt operates more smoothly. It opens and closes much easier than my 710.

The other major change is that the receiver doesn't have the nylon (plastic) insert and is all steel. The later 710s dropped the nylon insert in the receiver and the 770 continues the all-steel receiver. I never knew what the big dot deal was about the nylon insert, but a lot of folks didn't like it.