If you run on a Remington action, ideally a .338 RUM would be better, where as the Lapua would be better served on an action designed for a lapua based cartridge, due to concerns of lug set back.
In contradiction to this, I built a .338 Norma on a remington action. The side affect is I have to be very careful on my loading to keep them relatively mild, I try to stay at or below CIP rated pressures, though I am only going by educated guess. Thus, I usually don't get the same velocities many other people get that just load up to pressure signs and back off a little. My current load is a 250 at 2877 from a 24" barrel.
Also, pressure signs in Peterson or Lapua .590 bolt face brass usually doesn't appear until you are way over rated pressures, as it is very tough stuff, making it more challenging.
When I burn out this barrel, I will either rechamber to .338 RUM or EDGE, or get a different action to run the Norma. As of now, I don't have any of the noticeable lug set-back issues you sometimes hear about, and have around 500ish rounds through my rifle, but wouldn't be surprised if I end up with a measurable amount when I get it rebarreled.
If you don't mind getting a different action, I personally would go for the Lapua of those two, similar performance, however the Lapua or Peterson .338 Lapua brass is stupid tough, and you have that much more brass around the primer pockets to keep them tight in comparison to the EDGE, similar to running a small rifle primer pocket vs large rifle pocket on say a 6.5 cm, the srp will hold up longer than a lrp pocket, assuming same pressures are being ran. If you don't mind fireforming, a .338 Lapua Improved +P would be awesome as well, extra performance and less trimming. ADG or Peterson brass for the .338 edge would also be super tough though, there really isn't a bad choice in the proper action. Sorry for the novel!