The 338 Norma is based off a shortened 416 Rigby case. It's shorter and more efficient than the 338 Lapua, it's main purpose is extreme long range sniping and is a NATO round. The above rifle I would shoot out to 2500 yds regularly.
In a sporter weight rifle it's going to be pretty stout recoil. Factory ammunition is all match hollow point ammo, if you reload not an issue. Lapua and Norma brass is readily available.
Unless shots past 400yds are in your future I would opt for the 338 win mag, much more versatile and available.