Unfortunately most airguns these days are very small caliber. You can take a .177 and increase the muzzle velocity as much as you can but it still won't do much damage even at 1.000+ fps. Also, the pellets are really light and become unstable at very high velocity. I just checked around and it seems even a powerful .22 air gun doesn't come anywhere close to .22LR.

Seriously, when you consider that a "magnum" air rifle is every bit as large and heavy as a .22LR carbine but far behind in terms of power you need to ask yourself if it's really a viable choice. Even in a situation where firearms are out of the question there are better alternatives IMHO. You could get a very good crossbow (something like a recurve Barnett) for under $200. It's just as quiet and low profile as an air gun but far more lethal.

I still think a large caliber air gun would be a great survival rifle. But they tend to be very expensive these days and all operate on the PCP principle, so you basically need a powered pump and scuba tank.