In 338 RUM, it looks like a 250 grain Berger at 3.75" magazine length is still going to be intruding on the case capacity with the base of the bullet. A 338 Edge is going to intrude 0.090" more but it looks like it tends to have a longer throat so you might wind up with a huge jump at magazine length.
When I looked at load data, it seemed like a lot of recipes were similar. Maybe the extra case capacity of the Edge reduces pressure but it didn't seem like RUM has a big disadvantage unless it's compared to a +p and then you are burning a lot more powder and RUM might not have the case capacity to take advantage of a +p throat.
I didn't feel a need to go to Edge.