An air rifle is surprisingly powerful. I've got a .177 advertised at 1000fps, breach break, single pump. I don't think it's actually 1000fps, but it will send a pointed pellet clean through 5/8" of plywood from ten yards.
Compressed air as a power source for projectiles is comparable to ignitable powders. In the 18th and 19th centuries air rifles in something like .30 caliber were used for hunting and by some armed forces. Large animals, moose, elk, stags, etc., were regularly killed with these guns. Merriwether Lewis, of Lewis and Clark, brought an air rifle, .30 caliber or so as I recall, along on the expedition and never failed to amaze Indians with it.
I've wondered why manufactures don't make air rifles in larger calibers today. They certainly could if they tried. My guesses are that they anticipate legal restrictions closing down their markets quickly, and/or that rifle-sized air guns in larger calibers lag much more behind modern powders than older air guns did their black powder contemporaries. But I don't really know.