ORIGINAL: James B
While one rifle could do all these jobs, none would be ideal for everything. Out to two hundred yards, all three would serve well. I look at things a bit differently when it comes to big guns. If a 30-06 won't do the job for big bears, then I want a 375 H&H or 416 Rem Mag. I will skip over the medium bores. For all North American game if I was starting from scratch, I would buy a 270 or 280 and a 375 H&H. The 270-280 rounds are not bad for recoil and shoot fast and flat for deer and antelope and the 375 shoots flat enough and has ample power for the really big mean stuff.
If I had to pick just one of the mentioned ones, I would pick the 30-06. This because I don't get any enjoyment out of shooting the 300 or 338 mags when 99 percent of the time the extra power is just not needed. The recoil of the 30-06 is more than I enjoy as well. However it is acceptable.
I have to agree with James on this one