From what I have measured in case capacity, the Lapua and the 338 Edge are basically identical. Some lots of brass will give the Lapua a 1 to 2 grains capacity advantage, other lots will give the 338 Edge the same slight capacity advantage.
Simply put, when loaded to same pressures in same barrel length with same bullet, they are ballistic twins. Which is the fastest will depend more on barrel variations then anything to do with the case itself.
The Lapua has an advantage in a stronger case that will have a longer case life but they are alot spendier then the 300 RUM cases as well.
The 338 Edge has the advantage that it can easily be loaded into any receiver that is a true magnum length receiver without much modification. That is not the case with the Lapua.
Ballistically take your pick, they are the same. Loading wise, again, take your pick, they are both easy to load for and neither require any fireforming.
The 338 Edge just allows you to use a larger variaty of receivers. The Edge is however a long round and best suited to the Rem 700 receivers with a Wyatt extended mag box. The Lapua on the other hand is fat and works best with center feed mag box designs such as the HS DM system.
They both have pluses and minuses, in the end they both throw the same bullets to roughly the same velocity.
The standard 338 RUM will run 75 to 100 fps less then either of them with same pressures, bullet and barrel.
Kirby Allen(50)