The battery life on the remote is what you make of it. I've had it last for over a week on a single charge.
The color screen is nice if you're looking to do any customizations like favorite channels using the channel's logo or something like that. Other than that, its just pretty. (I find it easier to read)
I also find the 880 much easier to program custom tasks. (sorry...this is the 880 compared to the 676)
Overall (if you can't tell) I prefer the 880 to the others, but the biggest difference you'll notice is the button layout. Get your hands on them and check out the location of your favorite buttons...that'll help you decide. (For example, the 676, the DVD control buttons are high up on the screen, as compared to the 880 where they're in the middle of the other buttons, but with fewer buttons to look at...vs. some of the others that had the DVD buttons on the bottom, making them awkward to use.)
The biggest thing I dislike about the 880 is the blue glowy-thing on the cradle. I hate blue lights on electronics. I find them to be visibly distracting from whatever else is going on, particularly in a dark room. So when I'm not using the cradle, I unplug it.