FWB 300S .177, 5 shots at 35 yards, with 8.4 grain JSB Exact, generating about 6fpe at the muzzle.
I talk to guys all of the time, that are coming over to airgunning from a lifetime of shooting powder burners, and the one thing they are almost always focused on is pellet velocity.
Show them an airgun, and the first question is, "how fast does this thing shoot a pellet?" That's usually where the education about the differences between hunting with small bore airguns, and small bore powder burners begins, with the emphasis on accuracy, not power.
Small bore powder burning cartridges, like the .17HMR, .22 Mag, .223, .22-250, and .220 swift, are high velocity death on small vermin like ground squirrels, and prairie dogs. Highly explosive projectiles, such as the Hornady V-Max, and Nosler Ballistic Tip bullets, when driven at high velocity, literally detonate small rodents on impact.
At impact, a tremendous amount of energy is released by the polymer tipped bullets rapid expansion. I have hit ground squirrels with a 50 grain V-Max bullet, fired from a .22-250, doing over 3500 fps at the muzzle, (1360 fpe) where there was literally nothing left of the squirrel but red mist and hair blowing in the wind. Impressive power to say the least. You're not going to get that with an airgun pellet. Hunting with small bore airguns is about accuracy, and very precise pellet placement, not high power.
When shooting powder burner varmint rifles, supreme accuracy was always a pursuit of mine, but for a slightly different reason than when shooting my airguns. Supreme accuracy, lets met reach out farther with my powder burners, 400 yards and beyond was common. I wasn't so much concerned with placing a Ballistic tip bullet on a precise spot, like the earhole of a ground squirrel, as I was mostly interested in putting it center of mass, on the squirrel or prairie dog at long range, and the highly explosive bullet would take care of the rest.
With my airguns, I also pursue high levels of accuracy, but with these guns, it's because I need to place a pellet precisely where I want it to go. Airguns do not blow things up, they kill by putting a pellet through one or more vital organs of the critter being hunted. That means a high level of accuracy is required, to consistently put a pellet precisely where it is wanted, on demand.
The guns I hunt with, all have one thing in common. They are very, very accurate. The power levels vary from about 6 fpe on the low end, to 46 fpe on the high end. Not enough power to vaporize rodents that's for sure, but still enough power to kill cleanly, within each guns accuracy capabilities and power limitations.
For example, the above photo of a target, shows a five shot group at 35 yards, fired from one of my FWB 300S, .177 cal, recoilless springers. This gun generates about 6 fpe at the muzzle. The orange dot is half inch. This rifle is death on ground squirrels, with head shots out to 45 yards.
A typical adult California Ground Squirrel, or adult Gunnison's Prairie Dog's head, is a target that measures roughly 2 inches wide by 2 inches high, and about 2.5 inches front to back. Inside of that, you have about a 1.5 inch kill zone. Include the neck, and upper chest, heart lung area, and we now have a kill zone that runs about 1.5/2 inches wide by about 4 inches tall.
Not an impossible target, all the way to 100 yards, but it takes a very accurate airgun to stay inside that 1.5/2 inch wide kill zone at that distance. Especially when shooting in the wind.
Depending upon where and what I'll be hunting, I use various guns that all have excellent accuracy, but cover a wide range of power levels.
If I want to reach out a bit farther than my 6 fpe FWB 300S allows, but want to hunt a gun that's short and light, I'll grab my Marauder pistol/carbine.
Below target, Marauder .22 pistol/carbine, 5 shots at 40 yards, with 12.8 grain Sn-2 tin pellets, generating 13 fpe at the muzzle.
I'm very comfortable using my Marauder pistol/carbine, for heart lung, or head shots on ground squirrels out to 65 yards. The accuracy and power, at 13 fpe, is more than enough for California Ground Squirrels at that range. Last year, I used it exclusively for hunting ground squirrels, and the performance was simply amazing.
If I'm looking for a bit more power, and reach, in a nice light rifle, I'll hunt with my Benjamin Discovery.
Discovery .22, 5 shots at 30 yards, with 16 grain JSB Exacts, generating approximately 23 fpe at the muzzle. 
My Discovery has been a ton of fun to hunt with. The accuracy and power, let me take ground squirrels out to 75/80 yards, and the light weight of the gun makes it a dream to carry all day long.
Below are other sight-in targets from some of my other hunting PCP's. The power may vary from gun to gun a bit, but the common denominator through out all of these PCP's, is their excellent accuracy.
There is also a wide range of gun prices represented in this blog story, but accurate, is accurate, whether the gun cost $250, or $1600. That doesn't matter to me, because I'm mostly interested in what a given gun can do down range with a pellet. That's where the real work gets done with any gun, and my less expensive PCP's shoot right along with some of their higher priced cousins.
I've used all of the following guns to take ground squirrels, and prairie dogs out to around 100 yards. The targets show the performance, of each gun, when sighted in with its tested pellet of choice.
RWS Rapier .22, 5 shots at 50 yards, with 18 grain JSB Jumbo Heavy's, generating 30 fpe at the muzzle.

AA 410ERBSL .22, 5 shots at 50 yards, with 18 grain JSB Jumbo Heavy's, generating 30 fpe at the muzzle. 
Benjamin Marauder .22, 5 shots at 50 yards, with 14.5 grain DYNAMIC PCP-2 tin pellets, generating 27 fpe at the muzzle. Half inch orange dot.

AA 510 TC .22, 5 shots at 50 yards, with 18 grain JSB Jumbo Heavy's, generating 29 fpe at the muzzle. 
Benjamin Marauder .25, 5 shots at 65 yards, with 30.8 grain Beeman Kodiaks, generating 46 fpe at the muzzle. 
FX 2000 .22, 5 shots at 100 yards, with 21 grain Beeman Kodiaks, generating 31 fpe at the muzzle. Red dot is one inch.

With the exception of the .22 cal Marauder, none of these guns are driving their pellets over 900 fps, and a couple, the Marauder pistol/carbine, and FWB 300S, are under 700, and 600 fps respectively. Not tons of power (13 fpe and 6 fpe) for sure. Yet both guns are very efficient killers of California Ground Squirrels.
Anyone who has followed this blog, the past several years, has seen stories, and videos of these guns being used to hunt with, and when used within each guns capabilities, and power limitations, they have all performed the task at hand very, very well indeed.
All of these guns are superbly accurate, and that's the focus when it comes to hunting with small bore airguns. We need enough power, along with the accuracy, to deliver a pellet cleanly to the vital organs of our chosen prey. We will never have the kind of velocities and power, that the powder burner varmint cartridges generate, but we don't need them either.
Hunting with small bore airguns, isn't about high velocity and loads of muzzle energy, it's really about accuracy, and precise shot placement, and for me, that's what makes it so challenging and fun.