As to the .300 RUM vs. .338 RUM question, examples are based upon a 200 yard zero and all availableload data that I have. I ran these calculations back when I was debating over .300 Win, .300 RUM, .338 Win, and .338 RUM. The results were interesting and eye-opening for me, to say the least!
.300 RUM, 200 grain XFB, BC = .550, 104 grains H870, 3028 fps, 17.2" drop at 400 yards.
.338 RUM, 200 grain Ballistic Tip (sorry not exactly the same bullet), BC = .414, 88.7 grains IMR 4831, 3160 fps, 16.8" drop at 400 yards.
The .338 RUM in this case is faster and shoots flatter at 400 yards than the .300. At extreme ranges the higher BC of the 200 grain .300 will start to do better, but then if you want to go to longer ranges you'd go up to a 250 or 300 grain pill in the .338. My .338 RUm can do +3200 fps using 225 grain bullets, and +3100 fps using 250 grain bullets, so I'm not surprised by the results.
As for recoil, plug the above loads in and see where they fall. The .338 is slightly easier on the shoulder, which is counter-intuitive. The higher powder loads in the .300 create the higher recoil numbers, even if you use heavier bullets!
If my calculations are wrong, or if someone has any better information, let me know, I'm all ears!
Mark in Utah