Here are case capacity and case length for several popular 338 Cartridges.
cartridge______ grains inches
338 Federal ___57.5 2.014
338 Win mag____ 86 2.500
330 Dakota_____ 94 2.530
338 Norma Mag-106 2.500
338 Lapua Mag-108 2.724
338 Rem Ultra_ 110 2.760
338 Edge_____113 2.850
338-378 Wby _- 137 2.910
Consider seating depth of the bullets you want to shoot and the magazine length you have available with the action you choose.. I don't like any cartridge where the shank of the bullet is seated inside of the neck- shoulder junction of the case. I find that seating deeper gives inconsistent velocity and I believe it can be dangerous. Also any 338 cartridge looses 2.27 grains of usable case capacity with each 0.1" of seating depth.
Of those I shoot 338 Federal, 338 Win Mag, 338 Norma Mag, 338 Rem Ultra and 338-378 Weatherby. Each has advantages and disadvantages. ":Best" depends on what you want to use it for.