What species of bear, and which species of caribou?
The American bears, I am told, speak with an accent, which the Canadian bears don't have!
I think that Canada has the edge for caribou, just because of the land mass that these herds cover.
If you are after black bears, I think Canada gets the edge there, too, just because of the area where this species can be hunted, in Canada.
Grizzly Bear, I don't know. Alaska may have a longer season, or more animals which may be harvested. Grizzly in Canada would require a guide, and trophy tag, so it gets plenty expensive.