Ian, Ken Waters tested a 338-308 in Handloader Magazine a few years ago. I don't recall the exact velocities, but as I recall, a 200 gr. bullet could be run 2500 fps. You could likely find the back issue of the handloader magazine at their website.
Good luck,
35W

I had a Winchester Model 88 rebored from a 308 to a 338-08.
I use 200gr. Hornady and 200gr. Ballistic Tip's. I even tried some 200gr. Hornady Flat Points.
I figure I get between 2500 & 2600 fps from my loads.
The gun has some interest, Dick Nickles was in the middle of the rebore job when he passed away. The rilfe had to be sent to Cliff LaBounty to have it finished up. Two great smiths worked on this gun and it shows it. Very accurate with an excellent bore.

Didn't Winchester make a 28 cal. cartridge based on the .308 case?

Uh..I don't who made it but its called a 7mm-08