It really depends on which emergency situation you’re most concerned about surviving. Irt also depends a bunch on where you live and how modern your POTS system is.
Generally, none of the systems will survive local EMP. The idea that the Internet is somehow nuke-proof is urban legend. The design concept of a re-routable network WAS intended as an affordable way to build in redundancy for a theoretical nuke-survivable government comm system.
But the real Internet as implemented today is NOT in any way nuke hardened. All the nearby parts will fry in an EMP event. So if a hefty nuke goes off at low altitude within say 100 miles of you or where you’re trying to connect, forget it. OTOH, the internet 1000 miles away will be mostly unaffected. If, for example, a nuke hit DC, then Seattle could still communicate with Chicago even though Baltimore couldn’t communicate with anybody.
In many disasters the real problem isn’t physical destruction of the network, but simply overload as everyone tries to call somebody at once. this is particularly true of terrorist-type events where the actual destruction is tiny, but the public is highly agitated.
The actual destruction on 9/11 was trivial on a national scale and minor even within the confines of NYC & DC. But the hornet’s nest of very upset people was in the 10s of millions, most of whom reached for their phone.
VoIP, provided the other end of the call is either also a VoIP subscriber, or is well outside the affected area, probably has the greatest surge capacity, assuming the disaster itself hasn’t damaged the local network.
But how is your VoIP signal carried? If you’re using a basic modem or DSL, it’s traveling over the same physical network as the POTS. If the telco has lost a lot of wire up on poles (say hurricane or ice storm or earthquake) or their underground tunnels are flooded (say hurricane or river flooding or earthquake) then you’re still stuck.
Conversely, if your IP connection is via cable TV, well, much of their infrastructure also is strung overhead on poles in many areas. Elsewhere the cables run underground in the same tunnel network as the telcos use. Same vulnerabilities.
Cellular uses radio to go from your handset to the local tower, then conventional in-ground or on-pole cables to get to the telco switrching center. So it has all the same weak points as POTS, plus the possiblity of tower collapse, etc.
POTS depends on power provided by the telco switch, and they have very robust long-lived backup power facilities. They can operate through extended blackouts.
Cell towers have only short-term backup, and the telcos can’t keep up with replenishing the diesel fuel at all of their thousands of towers in a widespread blackout. As long as you’re not using a wireless portable at your end, your POTS will last indefinitely.
VoIP depends on power both at the switch and at your end. Without a backup generator for your computer, etc., you’re out of luck.
Bottom line: No one choice is “better” for all scenarios in all locations. VoIP has the most local points of failure, followed by Cell and POTS. Cell has the best portability; if the lines are down at your home or office, VoIP & POTS are useless, but maybe you can drive 3 miles to find a live cell tower.
The most robust choice is to have all three. And backup power generation at home and office. And spare fully-charged cell batteries and a full tank of gas in the car. And a laptop with VoIP software loaded. And finally, to realize that if there’s a real disaster happening near where you are, calling somebody is probably the least useful use of your time and energy.