I’m not an air gun guy but these entry level PCP’s (marauder, gauntlet, etc..) have some of my attention. I want something for rodent control, introducing kids to shooting, and a cheap alternative to long range precision shooting. I want it quiet. I’ve already got a pretty good bolt gun (308), an SBR AR equipped for NV use, a few 9mm handguns, and a couple centerfire suppressors. Next logical step for powder burners would be a rimfire Rifle and/or pistol with a rimfire can.

What can a PCP do better than a suppressed ruger American rimfire or suppressed 22/45? The ultimate answer would probably be get both, and someday I probably will but for now one has to take priority. Help me decide. Thanks!

Out to about 40-50 yards, the air rifle, once tuned to your specs; will probably be more accurate.

The cheap ones need work.  I have a Gauntlet and was about to alter it against a tree before I found the best way to stop the point of aim change they are famous for.  Not a barrel band, but an added spring to the moderator at the muzzle end of the gun.  Now it shoots one hole at 40 yards.

The initial investment in the air rifle will be a bit more.  However, the savings of the ammo will offset this in short order if you plan on shooting quite a bit.

Advantages to the air rifle:

Generally quieter
Cheaper ammo
Shorter safety range required
Often legal to shoot where powder burning rifles are not
No brass litter
No hazmat shipping of ammo
Long range practice is shorter

Disadvantages:

Substantially less powerful (with .25, for example, you are pushing out a 25 grain pellet at 850 ft/s while a .22 standard velocity rimfire shoots a 40 grain bullet at 1050 ft/s)
Need a source of air, either a tank or hand pump.  If tank you need a convenient place that will re fill it, and a device for filling which connects to the tank  
Good ammo will need to be ordered rather than picking some up at the local shop (unless you have a specialty air gun store nearby)

My PCP gun is an Air Arms S-500; so mid-range as far as price goes.

I didn't skimp when I bought the rifle or the associated gear such as air tank and optics; but I have a lot more money in the air gun than I do in my .22s and the suppressors. That being said, you don't need a tax stamp for the air gun and thus you don't have the significant wait time waiting to get the stamp.

Depending on your circumstances, getting the air tank filled is sort of a drawback. Unless you spend a significant amount of money on an air compressor capable of the pressure you need for these guns, you need to find a place to fill it. And I have had occasion where I wanted to shoot and my air tank was empty (I guess this would be the same as wanting to shoot and not having ammo). In my case, I am a retired firefighter. I live in a small town where the guys at the fire station know me (I am not retired from there,but..........) and they fill mine. Most guys go to a dive shop to get their's filled, which here is about 35 to 40 miles away. The air tank I have will last for a couple months at the rate I shoot FWIW but it wasn't cheap. Even the cheap ones, arn't cheap. FWIW: these PCP airgun compressed gas cylinders are the same thing used in firefighter's SCBAs.

The air gun is nice in that it can much more safely be shot in the basement/garage regardless of weather or in the backyard with less of a backstop than would be safe with a .22. I wouldn't want to shoot a .22LR in my basement mainly because of the smoke/lead contamination.

Relatively speaking, I would say the sound of the report of each is about the same.

My air rifle is SIGNIFICANTLY more accurate than any .22 I ever fired. I shoot mostly at an indoor archery range (no wind, constant temperature). If I am on my game, I can shoot groups at 30 yards the size of a single .177 pellet. One hole at 30  yards.