My 338 WM Rem 700 SS 24" barrel through my chronograph goes 2935 FPS. It was 2928 through another chronograph. 225 gr. Nosler Partition.
I have shot this load since 1994 in this rifle as a hunting load. This load was low in old books, but right at max with todays loading data. Primer pockets are tight and bolt opens easy every shot.
I checked all my loading books. They list the 338 WM at 150 to 200 FPS faster in their data bases. than the 338-06.
Ammo availability will mean a lot also. Only a couple companies list 338-06 ammo.
If you are traveling with the rifle hunting. Guns Shops I have been in in Alaska and Canada stock 338 WM Ammo. Seen one store with Hornady 338-06 in stock.
Good Luck in your choice, Happy Shooting.