While hunting big game the only handgun I would consider carrying is a 22 revolver. When the action is slow it's nice to be able to pick off a grouse for the table.
I hunt in an area that is known for it's big black bears and I've never carried a backup handgun. If I can't do it with 7 rounds of 30-30 or 12 rounds of 357 magnum from my carbine I don't see what good a pistol is going to do me. If I hunted in an area where meth labs or marijuana farms were known to be I would be much more likely to carry a handgun or maybe just a bunch extra ammo for the rifle.. . .if I hunted there at all!
However, if I'm not hunting my woods handgun is usually a Smith and Wesson Model 10 or my Ruger Blackhawk in 357 magnum. It all depends on my mood.