The 338 or 340 would be my first and only choices for one rifle on an Alaskan hunt. The big bears take a bit of thump to stop at times, and the 338s can reach way out if necessary on the sheep hunt.
If you have the 300Win, but no 338...don't go to the trouble and expense of getting one. The 300 will do fine. I would have two different loads and scopes for each in GOOD QDs....165s or 180s for the sheep, and 220s for bear...