Mike,
Where is your primary area of hunting?
As stated above, I carry both. Usually a centerfire or 22mag on a bipod and a shotgun on my lap. Switching involves moving one hand from the grip on one gun to the other, very little movement. The rest, shooting either gun, involves the same amount of movement no matter what. I have seen VERY few situations where a yote will come in directly in line with the muzzle of my gun. Even then, I still need to raise the butt to my shoulder and aim.
As far as too much to carry, I often tote both guns, my foxpro and decoy, my "chair" (one of the soft foldups with side support straps) and a bunch of other nonesential BS. Most is hauled in a fanny pack or backback. Usually the shotgun on a sling, rifle in one hand, seat straped on my back, and the rest in the pack. It is quick to load, easy to transport, quick to setup and quiet to move with. Some say its too much to carry. The only thing that changes is about 7 lbs. on a sling. Not a lot in the big scheme of things.
B