I can't honestly claim a "favorite" caliber. Each of my guns is a favorite for some specific task. For example, for serious competition I use a heavily modified T/C Hawken with a Green Mountain Barrel with 1/72 rate of twist in .50 caliber. It's won any matches for me in the 27 years I've been shooting it. It's also a fun rifle for hunting caribou.
Alaska hunting regulations require .54 caliber or larger if hunting moose, bear or other large animals with a round ball. For most of my big-game hunting I use a custom built .58 caliber trade rifle. The most accurate load for that rifle is 120 grains of Goex FFg under a .575 round-ball patched in tallow-lubricated linen. That load allows me to shoot eight inch groups at 120 yards with no problem and it will kill anything I'm likely to encounter. On the other hand, it's a heavy gun to carry around all day (nearly 9 lb) and with that narrow butt-plate recoil can be brutal. Not something you want to shoot all day on the line.
The most common gun I carry in the field is a 20 gauge (.62 caliber) smoothbore, either a reproduction Tulle de Chasse or my shortened (24 inch barrel) trade-gun. I carry the Tulle nearly all winter long, shooting grouse, hares, foxes and beavers. I wouldn't hesitate to harvest either a moose or black bear with it. At ranges under 50 yards I shoot it just as accurately as my rifle, it's light weight (just over 7 lb) and has provided me many meals on the trail.
During summer, when the only open hunting season is for black bear, I usually carry the shortened trade gun, primarily for defense against grizzly bear should I be so unlucky as to encounter one during a trek. Loaded with shot, it's also harvested a few grouse and hares.
Swanny