If you are gonna go 338 I would suggest the 338 win mag or up. You need horsepower to push those heavy bullets, that equals case capacity. If you are interested in long range (I assume you are since you asked about the Scenars because of their high BC) you need to go faster than 2400fps. If you are just looking for a lighter weight or less recoil, I agree with Dave Wilson's comments, maybe something in .30 cal would be better.
Now for your actual question on the Scenars. I have used them in my 338RUM, 338-378, and 338 Kahn. They shoot very good. I also achieve the same accuracy with Sierra Match Kings in the same weight, which are a 1/4th the cost. I have not used the Scenar for game but have used the SMKs on several deer at ranges from less than 200yds to 700yds. They have performed well in all cases, although there are some on this site who do not like them for hunting, others do, and I am certainly not trying to rekindle that argument here /ubbthreads/images/graemlins/grin.gif