Presuming big-bore means "Starts with .4 or bigger"...
Favorite? Tough question, as I have many choices, from .41 mag to .50 A.E., in revolvers, autos, and single-shots.
After some consideration, I shall defer to my sentimental favorite, which also happens to be a gun I shoot very well for some reason.
It's a Webley Mk. IV, currently wearing a 6" Mk. VI barrel. It's been converted to run on .45 ACP and is sporting a very pretty set of grips I made out of the wildest-grained piece of mahogany I've ever seen.
Built in 1914, and serving through the Great War, (Through it, not neccessarily IN it.
) it has Style, History, Panache, and Character.
Or it's quite old, and really funny-looking, depending upon your viewpoint.
And me with no camera. Rats.