I firmly believe that .50 cal and above have definite benefits over anything smaller in bore size, although a .45 rifle will work for the game listed.
: In muzzleloading rifles, round balls kill perfectly. Slugs merely extend the distance of the tracking job.
: .50 cal balls of .495" weigh approximately 184gr. in pure lead. Pure lead is what is required below about 20 bore size. A .490" ball may be used in a .50 cal. as well, with slightly thicker patches & will weigh approximately 4-8gr. less.
: A .535" pure lead ball weighs some 235gr. and is preferred for larger game like Moose and Elk. The .54 kills smaller game like deer and goats in it's tracks - with round balls. A .530" ball, also useable, weighs around 528gr. Slugs in .54 generally kill slower.
: Larger calibre than .54 is not needed for imtermediate big game as noted, but personal preferences abound.
: Personally, I prefer my .69 for all game shooting as well as target shooting. It is amazingly accurate, and will embarrass most modern rifles with it's 100 meter accuracy of 1 1/2" with OPEN sight 5-shot groups.