During our last extended (3 day) power outage, I was surprised to learn that even though I have all of my gear on a very large UPS, the cable network also ceases to function after a few hours. Local nodes apparently only have backup power for a short time. To their credit, I saw Comcast deploying small gas generators to nearby street poles the next day.
The cell network, on the other hand, continued working without a hiccup. This might have been because the nearest cell tower still had power, but even if it didn't, I'd assume that I'd just be able to connect to the nearest in-range tower that _did_ have power.
We had the same thing for a couple days recently as well. I actually went and topped off the generator in the morning as the cable company had let it run out of gas. I believe it is a regulation in being they provide phone service over their coax internet, and there are 911 requirements.
All of this, plus the lower noise floor during an outage means you can probably get usable signal from towers that would ordinarily be useless.
The cable network _should_ have many hours of backup, but they don't take it as seriously as the telephone network. Was built for entertainment, after all, so it doesn't have reliability in its core engineering.
The cell network, on the other hand, continued working without a hiccup. This might have been because the nearest cell tower still had power, but even if it didn't, I'd assume that I'd just be able to connect to the nearest in-range tower that _did_ have power.