These are not little critters and they are not cute little cuddly things. These critters are predators of the highest magnitude that can make your day turn sour very quickly. That said, the largest, most powerful cartridge is the way to go that you can handle and shoot accurately and effectively. If you can't handle a .416 Rigby, it will do you no good at all.
I would not go after these critters willingly without anything less than a .300 magnum of one sort or anther and most experts consider that a minimum. Sure, a 6.5 can kill a grizzly, but when hunting you must consider your weapon not only a hunting weapon but also a defensive weapon should the critter decide he doesn't like your antics. More than one story of two or three hunters emptying their large rifles into a bear and killing it, but the bear killing them before it died at their feet.
Most guides prefer .338 and larger caliber. Not my cup of tea any longer, so no need for me to hunt the critter. My .444 is not a great choice for hunting, but it works for me as a reliable round with enough penetration to do the job with proper shot placement. The gun feels comfortable to me and I know that with Buffalo Bore 335 gr bullets it has the penetration. The rest will be the luck of the draw and hoping I never have to use it in the first place, but it is a rifle I feel very comfortable shooting. That will be one of the most important aspects of rifle choice in the end analysis.