If you do your part a medium power .177 will do the trick. I know of two people who have accidentally killed large dogs with .177 pellet guns because they thought the small pellet would only sting the dog and they shot the dog to try to chase it away.If I do my part, will a 22 springer drop a big possum cleanly and humanely?
Years ago, a friend of mine lost his dog when a neighbor killed it intentionally with a pellet gun.
So they certainly have the potential to be lethal on fairly large animals. The key is good shot placement.
Unless we're talking about the high-end, larger caliber PCP air rifles which can be on a par with black-powder rifles of similar caliber, airguns don't kill with power, they kill with very precise shot placement. Even a very powerful airgun (again excepting the high-end PCP airguns) is quite weak compared to a .22LR firearm.
Powerful springers can be difficult to shoot because there is a LOT of movement generated by the power plant before the pellet even starts to move. Consistency is critical--the shooter can alter the point of impact by a few inches just by changing how tightly he grips the forearm of the rifle.The RWS panther is the best looking rifle of the group, fairly quick for reloads, is rated for 1000 fps. But unfortunately it is the least accurate by a huge margin. we have attributed the poor accuracy to the operator having to manipulate the barrel to break open the action then close the action possibly not returning the barrel exactly to where the rifle is zeroed for.
A decent quality break barrel won't have any significant accuracy handicap as a result of not having a fixed barrel. There are many other factors that affect accuracy in a spring piston airgun far more than any tiny variations produced by the break barrel design.
Mounting a scope on a springer can be problematic due to the vibration and springers can ruin scope not designed to handle the peculiar abuse a big springer imparts to a scope.
All that to say that the Panther is probably quite accurate--but it's probably a lot harder to actually achieve the accuracy it's capable of due to some of the issues that go with powerful springers.
Getting back to the OP, I'd recommend a PCP or a good pump since they're pretty easy to learn to shoot. The PCPs offer good power and much faster followups than anything other than CO2 airguns which tend to be much lower-powered than most other airgun designs. The downsides of the PCP rifles are that they're expensive and require some accessories (pumps and/or tanks).
I have a couple of pumps and a couple of CO2 airguns but most of my airguns have spring piston power plants.