Well, Everyone, thanks for the input. I fired them both side by side today. The Ruger Compact .243 handles great, is lightweight, and certainly accurate enough. Groups will probably shrink with a trigger job, and more handload exploration. The Browning A-Bolt 7-08 is an absolute tack-driver, and incredibly mild recoil-wise. After a few years of hunting with a magnum muzzleloader, a slug gun, a .450 Marlin, and .300 WSM, I have forgotten how much fun it is not to see stars after shooting 50-100 rounds!
Either one will do the trick with good loads and of course, good shot placement. I may let my wife use her 7-08, since she is new to hunting, and "borrow" her .243!