I know a little about air rifles and pistols, and have been party to several conversations as to their suitability for survival use. As with any tool, it depends on the scenario.

Be aware that it's hard to generalize too much about them, because "air" in this use encompasses at least 4 very distinct mechanism types, with several variations on each, and a huge range of available accuracy and power. The trend now is to using compressed air at high PSI, refilled from scuba tanks or expensive compressors. Personally, I consider all that too dependent on infrastructure to be of interest for survival.

There are some truly scary-accurate air pistols out there (they go to the Olympics, after all), but they're designed for 10 meters, and only the older models use hand-cocking mechanisms for power. Generally, in that kind of power range you're talking small-to-medium birds and not much else.

IMHO, the real limitations are inherent in it's being a pistol. It takes a LOT more training and practice for most people to become accurate with one. I'd say a shoulder stock was worth the weight and bulk, and if you're going to do that, you may as well take advantage of the length in leverage of the mechanism and the increased possible sight radius.. and you have an air rifle.

IMHO air rifles do have a place in a lot of scenarios. They can be compact, accurate, powerful enough for small game, SILENT, you can carry a year's worth of ammo in one pocket... and there are a whole lot more squirrels and bunnies out there than deer, and they reproduce a lot faster. They are also absolutely great for training/practice, and the marksmanship skills transfer well to firearms.