I've never used the 880. I've had the 720 before and as far as programming and ease of use the 670 is just as good, for me. The 720 cost me $170 and the 670 cost me $60 as a refurb from Amazon.
I really think remote preference comes down to the number of devices you have and the buttons you want on the remote. I prefer "hard" buttons for the commands I use most, DirecTV DVR and Volume. I also need something that is easy for my wife and daughter to use. Something they can use to turn on and off any combination of equipment - TV, AV receiver, Wii, DVD, Zone2, and Tuner.
I have the 670 programmed to operate for two different areas in the house, Family Room and Bedroom. This means it controls... 2 TV's, 1 AV Receiver, Wii, Vizio Soundbar, Zone2, 2 DVD players and 2 DVR's.
Two features I really liked about the 720 was it charged in the base and the backlighting came on automatically when you picked up the remote.
I guess a little more direct response to your question is... yes they both are programmed via a PC interface using Logitech's software. It's not really an internet app, it's installed on your PC and receives software and firmware updates via the internet.