I have AT&T's Uverse for internet, phone (their VoIP) and tv service. There are some known problems/limits with Uverse, but it matches my home needs. It also has never gone out due to a power outage on the AT&T side (including an outage that lasted for over a day for a large area around me).
Since we have their VoIP, they provide a dedicated UPS for the RG (modem/router/VoIP adapter). It is supposed to last for about an hour (IIRC), but I don't use it since the RG is plugged into the UPS for my home server and networking equipment.
During the long outage, the Uverse service stayed up the entire time. I had to recharge the UPS batteries a couple of times, but we watched TV and used the internet & phone through the entire outage. That's one of the nice things about AT&T, they have a lot of experience preparing for and running their equipment during power outages.