For the sake of argument, I think the .44 is the worst commonly-available caliber for the purpose of survival. The debate is situational to a great
extent (surviving a guerilla war requires different tools and skillsets than surviving a lonesome wilderness), but I think enough of the pros and cons
are universal to allow a discussion that's not completely apples and oranges.
So here are my reasons.
The rounds are heavy. You can carry thousands of rounds of .22LR or a hundred rounds of .44. The .44 takes up more room per round - a lot more room.
Unless you have a small truck devoted entirely to your ammunition, you're going to have to make sacrifices when it comes to other, critical items in
your kit.
The rounds are noisy. Very noisy. That's not something that matters at the range, but in a survival situation, you don't want your firearm of
choice to make a loud report (unless it's being used as a signaling device). It alerts others to your location, scares away game, and takes the edge
off your own sense of hearing.
The rounds are expensive.
The .44 has a lot of recoil (depending on what's firing it), compared to practically zero recoil from the .22. Recoil matters when it comes to
putting multiple shots downrange, with accuracy. Following up on that first shot is all important, and you can do it faster, and more accurately,
with a firearm that doesn't jump like a firecracker in your hand. Recoil also matters when it comes to women and children. I want my little girl to
be able to use our one survival firearm just as effectively as her old man.
The .44 will obliterate a ton of usable meat, especially on small animals. Small animals are the most plentiful form of game. If your cartridge of
choice is tailored towards medium/large game, you're going to be in a very unhappy place when you realize the relative scarcity of that prey. During
the 1920's in America, deer were all but eradicated in a very short period of time, thanks to hunters/poachers feeding their family. Deer will not
survive long in meaningful numbers in the face of the increased hunting pressure.
Anything that can be killed with a .44 can be killed just the same with a .22 - assuming proper stalking techniques and shot placement are not
ignored.
I can comfortably carry (and keep dry) literally thousands of rounds in a BOB, along with all the other essentials, and I don't have to sacrifice
other necessities.
If you absolutely must have a round better known for self-defense, then the .357 is a better choice IMO. It's more versatile, interchanges with the
.38, and will wreck anything it hits. Even the stupidly ubiquitous 9mm is better, simply because it's SO common.
I only see three advantages to the larger cartridges - whallop, fecal-factor (the ability to make people poo themselves with fear looking down a
barrel like a black hole), and ease of handling. I admit, it's downright miserable trying to navigate one of those little .22's into the receiver
with frozen fingers...
At the end of the day I think the clear winner is the .22LR, for all the reasons I've mentioned and more.
If your situation is different, say you're in a densely packed city and you don't plan on leaving, there are still more well-rounded choices in
handgun ammunition, like 9mm and .357. If it's a straight up warzone you want something with a much, much longer range, and more choices in
platform, something like the 7.62x54/39 or, heaven forbid, .223.
I could go on..but I won't.