Landlines (at least the old school ones that ran the line all the way back to a big central office, before neighborhood multiplexing devices were so ubiquitous) relied on very centralized infrastructure that was easier to keep running in a disaster, you only needed to keep one building powered to keep the town's landlines up. Sure, long distance service may have gone down when the lines outside the area were disrupted, but you'd still be able to call the fire department or your mom across town. And since that one building was so important, they kept a big generator there with lots of fuel.

The cellular network is much more disperse which makes it resilient in some ways (since if the tower closest to you goes down, you can still probably get signal from another tower), but it's harder to keep them all running, and in many cases they rely on long-distance data lines out of the area to stay in service, so even if the cell tower is up and running, without that long distance data connection, you can't make a call.