I had one made using a 308 WInchester Model 88. All that was needed was to rebore the barrel and a small change to the chamber. Shoots great, I like the 180gr. BT's and 200gr. Hornady.
I also shoot another 88 in 308 and a Savage 99 in 358.
To be honest I don't think you or the animal can tell a lick of difference, but hey, it's different, it's fun, and mines pretty darn accurate.

I bought a Savage M-99 real cheap one time that a butcher of a gunsmith had ruined the chamber on getting a stuck round out of it..I rebarreled it to a 338/284 as opposed to my initial idea of a 338-308 as it had more powder capacity and it duplicated the 338-06 very easily...It was a super nice saddle gun..and required hardly any action work...

Later I made 338-08 on a G33-40 Mauser action and it was pretty nice but I finally rechambered it to a 338-06 Ackley Imp....Had to go with the Ackley as the standard 30-06 will not clean up a 308 chamber...I found the 338-08 a bit lacking on velocity IMO....

Thanks for the input I will pass it on.
Im thinking it may be intresting to have a
upper built for a simi-auto AR or Fal type rifle.
I am currently having one done in 6.5-08
so it could be fun to mess with the .338-08 too.

Thanks
Tom