I can't speak for the .338 as I've only shot those that belonged to others, but the .340 gets your attention in a 8.5lb rifle.
Well, as a fella at the Sporty Whse was overheard to say, "It's amazing how much difference those two thousandths make."
I have so much trouble finding the correct bullets for my 340 that I have simply taken to wrapping .338 bullets with Scotch brand invisible tape to 'bump' them up. (Plain 'clear" doesn't work since they come in at .343") It's a lot of trouble, especially when I plan to spent an afternoon sniping bunnies in the willow thickets. What really sucks is the clean up afterwards
- the bunnies that is; Hoppe's #9 cuts Scotch tape fouling real easy.
As for the thread at hand however, I would only worry about the specifics of the rifle other than the caliber unless the 30-06 you already have is a solid stable 'Alaska-proof' design. (I enjoy blued metal and walnut, but there are times I really prefer something that needs no more care than a paddle.)