I have both air rifles and firearms. My opinion is that firearms would be vastly superior for hunting. Sure, you can take small game with an air rifle. But you can take it easier with a firearm. Hunting range for an air rifle is very short. You've got to be really close to your target. That alone makes things more difficult.

To get an air rifle powerful enough for humane hunting, you're going to want a heavy-duty springer or a PCP. But for "survival", are you going to have the air compressor and SCUBA tanks to support your PCP rifle? Probably not. So most likely you'd rely on a springer. Springer air rifles are more difficult to shoot well than firearms. They can be very hold sensitive. They have a harsh two-way recoil that can easily trash your expensive rifle scope. They're single shot. And they aren't all that quiet either. You shoot a hunting-class springer in your urban backyard, and your neighbors are gonna say, "Did someone just shoot a firearm?" Yeah, they're pretty loud.

I see air rifles as great tools for target shooting. Not so great for hunting. I'd put them in the same hunting class as a slingshot. Yeah, you can hunt with those too. And they're smaller and cheaper than air rifles. There's only so many squirrels and rabbits you'll be able to find for airgun hunting. Any game larger than that, and you're not really hunting humanely (despite the over-the-top Gamo advertisements where their .177 air rifle takes down a cape buffalo).

A .22LR rifle good enough for hunting is cheaper than a decent air rifle too.