I wish I had taken a pic of the ammo case in the store at Little Diomede when I was there a few years ago. They had 300 and 340 Weatherby, 338 Win and 375 H&H and a bunch of other stuff. ( A young kid had recently stepped out of his house one morning with his 308 to dispatch a white bear which was on the prowl for chained doggy treats.) I will say this for where I'm at, the 243 is highly rated, as is the 7MM Rem Mag, the 30-06 and the 300 Win Mag. The 375 is a popular whale (beluga) hunting round. And the 223, of course, sees a lot of use. Twenty years ago more of the little 55 FMJs were probably fired through Mini-14s than anything else. Nowadays the AR type rifles have become pretty common. Haven't yet run into any Inuit around here though, of course. Alaska has its own Eskimo cultures often generalized into three groups. PC hasn't quite convinced people to use the term sometimes used to generalize Canadian Eskimos. (That would be kind of like calling anyone of European ancestery a German, I think.)
