I've never actually owned a Tivo, so I can't say exactly what the differences are. But if you aren't familiar with either, I would just stick with what you can get from Verizon. Functionally, I don't think there's much difference between them anymore, and I don't think the costs are going to be that different either. I have FIOS as well, and I've been using their multi-room DVR with no issues.