Here is some Factory load data for the 338 Federal..
P338FA1 - 180 grain Nosler AccuBond at 2830 fps.
P338FC - 185 grain Barnes Triple-Shock at 2750 fps.
P338FB - 210 grain Nosler Partition at 2630 fps.
and some handload data for the 338-06
200 Nosler Btip RL 15 50.5 54.7 2,725 --
200 Hornady SP 58.5 62.8 2,705 Compressed
215 Sierra SPBT IMR4350 56.5 60.7 2,649 Compressed
225 Speer SPBT H414 CCI 200 Wby. 56.5 60.5 2,61
225 Barnes XLC Big Game 54.5 58.9 2,606
225 Speer SPBT Big Game 55.5 59.8 2,627
250 Sierra SPBT RL 15 46.5 50.4 2,464
250 Nosler Part. H414 52.5 56.8 2,475
not really any significant difference in the velocity... the only advantage I see is the ability to shoot 250 grain bullets because of the longer neck and powder capacity in the 338-06...