Some questions need to be answered first.
1. Do you need a .300 WM or .338 Lapua to accomplish your long range goals?
2. What is your idea of long range?
3. What is your experience level with rifles?
4. Do you reload or are you willing to invest in equipment and learn?
5. Do you own a Chronograph?
6. Do you have a place (shoot) to take advantage of a rifle chambered in .338 Lapua?
Number one is pretty easy, as there are a lot of cartridges that will get you long range shooting much cheaper than the two choices you gave.
Two, everyone has a different idea of long range to me it doesn't really start until you get north of 600 yards.
Three, with the two cartridges you selected you can't usually jump right into them and expect to shoot well.
Four, good quality ammunition for both is expensive. Far more so for the .338 Lapua. If you want to shoot you'll need deep pockets or reload to make it affordable long term.
Five, you'll need a good chronograph to measure your speed to work your drops.
Six, if your not shooting 800 yards and beyond all the time, the .338 Lapua is usually far more rifle than anyone needs.