What utah7/08 says makes sense;the 7 RM is a great general purpose deer/sheep/antelope/elk rifle,and with light bullets the 338 can "overlap" to back up on any of those animals; for bigger stuff,the 375 trumps the smaller cartridges but the 338 with heavy bullets comes close enough to back up the 375.
I like the 300's better than the 338 myself but no denying utah's combo will work well about anywhere,on anything here.