I have 2 big bore air rifles and both have taken big game. A .45 cal. Sam Yang and a 308 Exile by Dennis Quackenbush. Deer and wild hogs are no trouble for these two.
The Sam Yang is a production gun that with very little modification can produce well over 200 foot pounds of energy. I think that is approx. the same power as a 45 ACP. The .308 is a longer/flatter shooting custom gun that is capable of shooting coyotes at 125 yards. I guess they are not everyone's cup-o-tea, but I find them an engineering marvel and , well...just plain cool. As an added bonus, sound suppressors are readily available and completely legal on an airgun. This quiets them down considerably, as most bigbore airguns are very loud (think .38 handgun loud). 3500 psi of air being discharged makes a pretty good bang.