I have no experience with a 338-06 but have some with a 35 whelen. In my opinion, running something like a 250 grain bullet gives a bunch more recoil. Whether it is too much is a personal thing, somewhat based on the rifle (stock) in question. For me, an 8lb whelen is about the same as a hot 300 mag, maybe less jump but a fair amount of push on the shoulder. No way I'd run one with an 18" barrel, for a variety of reasons. (rifle balance, noise, and performance being only three) But then, there are very few instances where I'd be very interested in any 18" barreled rifle.
