Firecat, Before I retired I had a shop and a 1000 yard range outside the door of it. I built the 338-300 ultramag from late 98 until 2001 when the 338 RUM came out. I also did the Lapua and tested several versions of improving it. The improved Lapua is the best of this bunch in my opinion if you want a wildcat and will get you another 100 fps. Velocity wise, averaging many rifles, if you were splitting hairs there would be a slight gain in velocity from the 338 RUM to the 338-300 RUM to the 338 Lapua. I think the brass loaded to higher pressures may be what gives the lapua a slight advantage. We are talking maybe 20 fps between each one. But this would be taking the average of 10 rifles in each cartridge.
For one guy, getting one rifle built the accuracy load in either of the three may outperform the other. In other words it depends on your individual barrel and rifle. Some barrels are fast and some are slower. You may get a 338 Lapua that does best at 2725 fps a 338-300 ultra or edge that does best at 2740 fps and a 338 RUM that does best at 2850 fps. Interchange any of them into any of these velocities. Best load in any of them could be anywhere between 2725 fps and 2850 fps with a 30" barrel(or a fast barrel even faster). But that is the range for all three. That is why I say all three are the exact same thing. Accuracy wise they are all three extremely accurate and have not seen any of the three with an advantage there. I shot all three head to head many rounds on my range.
Again, if you are doing a custom rifles
there are others that will outperform these by 200-300 fps. The Lapua improved can get near 3000 fps and the improved 338-378 wby case and Excalibur can hit 3100 fps. All are accurate.