I used to have several bigbores, but sold them all except for my .457. I currently use three different rounds in it, a 180 gr sabot, a 300 gr solid, and a 425 grain solid. I've managed to take game with both the sabot and the 425 gr chunk so far....duiker, impala, and springbok....porcupine, too....in South Africa, and whitetail deer here in the US.
I took a feral hog, 120 lbs, in Texas a few years ago with the .50 caliber using 180 gr roundball.
As to range, I feel comfortable with 100 yards and under in terms of my own abilities. The deer I shot last Saturday with the 180 gr sabot was 40 yards away, and she went straight down.
If you go airgun hunting with the mindset of a bowhunter, you'll be just fine. Know your distance, know your gun, and success is bound to follow.
In KY, you have to use the gun as a muzzleloader, but there are no caliber restrictions that I am aware of. (Could be wrong about that). There is no requirement as to the propulsion of the bullet, so as long as you load from the muzzle, you can use an airgun.
Hope this helps some....
Randy