Personally, I prefer the Benjamin or Sheridan products. They're made in the USA, and are both rugged and powerful. They are also multi-pump rifles, so can be adjusted to the level of power needed.
Now, as if that wasn't enough, get this - - they can be had in .22 caliber!
Most "combo" pellet guns are in .177 caliber, which gives you a somewhat faster velocity. And there is merit in shooting both pellets and BB's from the same gun, but each usually shoots to a different point of aim and there is little the BB's are good for but popping cans.
But the .22 caliber pellet will also serve any target and practice purposes you may find.
BUT - the extra weight of the larger, .22 caliber pill, when driven hard, gives a knockdown punch the .177 pellets can't muster.
This is important when you're considering the weapon for predator deterrence/dispatch.
Back in the old days they used to say, "Beware of the man with only one gun." I wouldn't consider the .177 combo-gun for anything really serious when it comes to dealing with potentially predatory animals.
Just google the Benjamin/Sheridan air rifles.