according to Nosler's new book the best powder for the 338-06 is
210 grain bullet AA3100 58.0 grains 2412 fps
the 280 is
140 grain bullet RL19 53.0 grains 2902 fps
I have found that if I load 1 grain up or down it makes it more accurate for me.

If it were me I would load the 338-06 with
180 gr bullet and N150 55.0 GR 2834 FPS
this is 400 fps faster than the 210 grain