As those that attended my air rifle class during WCT know, there are no simple answers when it comes to air rifles. The choice of power plant, caliber, pellet, optics and rifle/pistol style are selected to make a shooting system that meets a specific set of criteria. Let's face it, shooting a house sparrow in a box store will be different than shooting a raccoon in a cage trap. Shooting a ground squirrels at 100 yards across wind blown fields will be different than shooting hogs in a capture pen. You need to match the right shooting system to the job at hand.
At times, a smaller pellet generating less FPE (foot pounds of energy) is the best option while at other times it is the exact reverse. You need to understand the animal, know the amount of energy required for a clean dispatch, understand the kill zone(s), be able to identify what are acceptable shots, determine your effective range for the kill zone with that particular shooting system, understand how the pellet is going to perform, and more. The reality is that 20 FPE is 20 FPE regardless of what caliber is producing it. So if a squirrel requires 4 - 5 FPE for a quick dispatch brain shot, as long as the shooter knows where the brain cavity (not just part of the skull, but the actual brain cavity) is for that species and the shooting system produces a minimum of 5 FPE at the point of impact, it really doesn't matter what caliber you use. Having said that, I commonly recommend using a .25 generating a minimum of 30 FPE whenever possible for the simple reason that the .25 is a larger pellet than a .177, .20, or .22, so it is a little more forgiving when the shot is not 100% dead on.
A .177 is just over 11/64" in diameter, a .22 is just under 14/64 (7/32)" in diameter and a .25 is 16/64 (1/4)" in diameter. It may look like a very small difference between 11/64 and 16/64 but looks can be deceiving as it is rather significant. Remember, that's a difference of 5/64 in diameter so the circumference of a .177 is actually 0.56 inches while it is 0.69 inches for a .22 and 0.78 inches for a .25. That's almost a 1/4" difference in circumference between a .177 and a .25!
Let's say you need to hit a 1/2" diameter target dead center for a quick dispatch (so room for error is 1/4" up or down) and instead your pellet impacts 5/16" low (so 1/16th out of the kill zone). If you're shooting a .177, most likely this is a wounding shot that will require a follow-up shot so the animal may not only survive, but also escape. If you're shooting a .22, most likely the shot will be fatal (you'll have a small amount of the pellet in the kill zone), but as it may not be immediately fatal there is a good possibility that the animal will run off and can't be recovered even though it will expire. If you're shooting a .25, again the shot will be fatal but more importantly, it will quickly dispatch the animal (as a good portion of the pellet will be in the kill zone) and give a good possibility of recover. Bear in mind that the above is in a perfect world and there are lots of areas where you cannot safely use a .25. In those situations, you may have to choose a lower caliber as the pellet will be lighter and thus have a flatter trajectory to the target than a heavier pellet.
As an example, let's say you cannot have more than 6 FPE at the point of impact on a target 20 yards away to ensure you don't damage material behind your target due to a miss or pass through and the pellet has to travel through a 12" opening between two boards on its way to the target. In this situation, you may have to choose a .177 shooting an 8.64 grain pellet at 558 FPS (feet per second) versus a .22 shooting a 14.3 grain pellet at 434 FPS or a .25 shooting a 19.91 grain pellet at 367 FPS. Although all three of these scenarios give just under 6 FPE, as you can see the .177 is almost 200 FPS faster than the .25 which means a much flatter trajectory allowing you to shoot between the obstacles. So even though the .177 pellet will have less killing surface than the other two, it is still the better caliber for this situation.
Lastly, you need to consider the type of pellet you plan to shoot. Diabolo or round/domed pellets are the best for longer distances as they tend to be the most accurate. On the down side, they also tend to penetrate through the animal so special attention needs given to safety issues. Remember that hollow point pellets don't act the same way that hollow point bullets do, but they still tend to create larger wound channels and not penetrate as far as diabolo pellets. This is where you really need to know your targets anatomy and what is required for dispatch. Although it is generally accepted that 10 FPE is required to penetrate a raccoon's skull, not all pellet types are capable of doing so at 10 FPE. For example, it may take 10 FPE for a 16 grain, diabolo heavy pellet to penetrate the skull but it may take 20 FPE or more for a 16 grain hollow point. Again, remember that FPE requirements are at the point of impact and not at the muzzle. So just because the manufacture claims your air rifle generates 26 FPE at the muzzle, it doesn't mean you can quickly dispatch a raccoon with it a 60 yards even if you hit the kill zone. In reality, based on pellet type, power plant and some other items, your 26 FPE air rifle may have an effective range of 10 yards or less for raccoon.
With pellets, performance comes down to the material the pellet is made from (some manufactures make harder pellets than others) as well as the pellet's construction. There are 41 different types of hollow point pellets sold on one Internet site (18 in .177, 16 in .22, and 7 in .25) and each one is going to function differently based on construction, distance from the muzzle to the point of impact, pellet weight, pellet speed, and what it hits. As a general rule of thumb, diabolo and cylindrical style pellets do good at penetrating bone while hollow point pellets tend to be better with heat/lung shots. Again, this is a general rule as it will vary from animal to animal.