Its extremely difficult to compare these two chamberings when we are dealing with different calibers, different bullet weights, different burn rate powders, different Sectional density bullets and different baring surface bullets.
There are several differing opinions on why this happens. We have had many discussions about these theories, some heated at times.
Some feel that the surface area of the base of the bullet allows this extra velocity, some feel its the faster burn rate powders that allow it, some feel its a reduction in baring surface with the larger calibers that allow this to happen.
Personally, I would say honestly its a combination of all of these factors. But still, we are comparing apples to oranges here which makes any meaningful comparision impossible to do.
So how could we level the playing field for a better comparison.
In my opinion, you have to take bullets of like design and same or similiar sectional density. The 200 gr 30 cal bullets have a sectional density of 0.301. IF we look at 338 bullets. The closest one we have is the 250 gr bullet with a SD of 0.313.
If you put a 250 gr bullet in a 338 Edge, the velocity potential will be EXTEMELY similiar to what you see with a 300 RUM and a 200 gr bullet. In my experience, 3150 to 3200 fps is pretty comfortable in a 300 RUM with this bullet weight in a 26-27" class barrel.
In the edge, a 250 gr bullet can be loaded to 3050-3100 fps in same length barrels pretty easily. So with bullets of same or similiar SD, the velocity spreads are MUCH closer.
No matter the opinion, its a simple fact that if you take two bullets of same weight, say 200 gr in 30 cal and 338 cal, the larger diameter bullet will be able to achieve significantly more velocity with same case capacity chamberings every time.
Again, I am sure its a combo of all these things that make it happen but the simple fact is that it happens and happens every time.
Same reason why a 375 RUM will smoke a 338 Edge in velocity when both are loaded with 300 gr bullets!!! The Edge will get you 2850-2900 fps but the 375 RUM will get you very close to 3000 with same bullet weight and do so in a 26" barrel length.