Arguably most powerful .22 air rifle is a Theoben Eliminator/Crow Magnum.
Depending on the pellet velocities can be well above 1000FPS. Generally these will run you into the mid to high 20′s in foot pounds of energy and at 50 yards, if you can make the shot, will put down small game of almost any kind (rabbits, birds, crows, etc.) with immediate kills. In fact, on most of these games, a good shot will go clean through even with a hollow point pellet.
However, this is just the beginning. When you get into Precompressed Pneumatic air guns, powered by a cylinder of compressed air filled from a compressor or scuba tank, you are driving the pellet with 3000 psi of gas. Rifles from Air Force, Ein Jin (As described above), Swivel Machine Works, and several others can run a heavy .22 caliber pellet into the 1000+ PFS range and start putting you into the 50 foot pounds of energy range for hitting power.
Still you are barely getting close to the power of a .22 Short, and still not at the level of a .22 LR.
Because gunpowder creates expanding gas at much much higher pressure than 3,000 psi. You just can’t get the velocities with pre-compressed air that you can with gun powder.
However you can compress alot of air in one of those tanks. So, where air guns start to excel is by pushing bigger bullets. If you start moving into .308 caliber pellet, or a 9mm pellet or larger you have a much bigger area to push on with your compressed air and you can have greater volume of air to push it with. So a large caliber air rifle still has very little kickback, but can have the kind of power you need to take down larger game.
ALL AIR RIFLES ARE NOT THE SAME