I like the Lapua for the brass quality like said above. But also you should consider if you even needed to purchase factory ammo. You will have a hard time finding it for an Edge. Like if you flew some where for a hunting trip and ammo was lost. Or, it was lost durring a pack in, heaven forbid.
My experience with the 338 edge and 300 gr bullets was not good with RP brass. About two firings and primer pockets were loose and brass went in the trash. That was with 92.5 gr of H-1000. I have fired the first 100 Lapua cases I started with 13 times now with the same 92.5 gr charge of H-1000. After even 13 firings the Lapua cases check out good and all 100 primer pockets are equally a nice tight fit. Some say Lapua brass is expensive, I say it is a value.
Also, the Lapua brass will need less prep right out of the box and will be more consistant.
Another point of interest is choosing dies. The Lapua dies are shelf stocking dies. Not sure what the best method for the Edge is, but I would check into this.
Performance is a wash between the LM and Edge, look for 2800 to 2850 depending on barrel and length, with 300 gr bullets.
What ever you choose, I recommend H-1000 and some of the new Berger Hybrid OTM's for bullets. Scary accurate!!
Jeff