I, as most on this forum; like different rifles and various cartridges. The ones listed in the title are some of my favorites.

For one rifle in Alaska, or anywhere else in North America with larger game and old school normal shooting distances; the 338 Winchester is my choice. It simply works very well, a bigger 30-06 in my opinion.
I use the 225 TSX in the 338 Win, but suspect the Tipped version makes this cartridge even more versatile regarding distance and wind. I have a Bunch of the non-tipped to load and shoot before I get to the tipped supply. I don't think there would any significant performance difference with 210 TTSX either.

I use the 270 grain TSX in the 375's, it works very well also. The 416's, I use the 350 grain TSX, but the TTSX version may be the better choice bullet.
The bigger bores do give me a somewhat easier feeling going through the alders, willows, and 5' tall grass. Purely psychological, but it's there.

Of the title choices, one rifle for all, then it is the 338 Winchester for me. If two rifles are in the budget, I would add a 375 or 416 in the same rifle platform. My rifles of choice are the Ruger stainless ones. Either way, a 338 Winchester would definitely be in mix.