As I've said before, when I started reloading, the little shop where I traded stocked Rem brass, Core Lokt bullets and CCI primers. And they worked so I've pretty much stayed with them. For hunting ammo, I suspect every case I've got sez Rem on the head. For target ammo, I think you can prep up Rem to match lapua but you're gonna pay some sweat equity to do it. With neck turning and weight culling and such. Lapua has recently reworked their machines and tightened up their specs, for their .223 brass at least, and it's now "Lapua Match". And it's specs are a lot tighter believe it or not. I don't know anything about their larger brass.
My experiences with Norma have been with .222 and 22-250. And they have been disappointing. If Norma and Remington brass were priced the same, I would buy the Remington.
IMO, if someone is buying brass to load for hunting ammo and is buying something other than Rem/Win/Fed/Horn @$25.00 a hundred, they're doing it to stroke their ego.
For match brass, if it doesn't come in Lapua or be fire formed from Lapua, I plan on spending a lot of time culling and prepping domestic brass.