Those Oryx bullets will do just fine on anything you shoot with that rifle. The only issue I have with them would be availability.
One thing to keep in mind about the 338 Federal, would be its strengths and weaknesses. It's a mauler out to 200 yards, it's trajectories with any given bullet weight past 200 yards resembles a rainbow. If you don't like bullets that pass all the way through, get a bullet appropriate for your needs. The Oryx bullets tend to expand very nicely at lower velocities.
I will say emphatically I LIKE THE CARTRIDGE. Long before Federal standardized the cartridge, it wasn't uncommon for wildcatters to neck up the 308Win cartridge to 338. Most of us called it the 338-08.
I don't use Oryx bullets in my 338-08 because they're expensive and difficult to find. I use Hornady 225 grn spire points interlocks, over 45 gn W748 and CCI 250 magnum primers. I've also used 225 grain Hornady IL SST bullets with the same load.
The rifle is based on a surplus K98 Mauser, fitted with a double set trigger, set in an early tupperware stock. The barrel is a take off Shilen, 6 groove, match grade, which was trimmed on both ends.
The barrel came to me at 28 inches long. It was rechambered and installed on the Mauser. IT WAS WAY TO FRONT HEAVY for my purposes, which was shooting from tree stands back in the day, shooting from blinds on small clear cuts and stalking along a few creek bottoms close by. The barrel was cut back a half inch at a time to see where velocity started to fall off. With such a large bore, unless you're using fairly fast powder there isn't enough velocity performance loss when reducing barrel length to worry about. It now sports a very handy, well balanced, 20 inch bbl. Knocking off the extra barrel length only brought about a measurable velocity difference of 50 fps, much to my surprise. It didn't even start to drop off until after the first 4 inches was removed.
This rifle is an honest two hundred yard point of aim shooter. The velocities with the 225 grain bullets is 2400fps+. The bullet drop at 300 yards is right on 20 inches, when sighted 1.5 in high at 100 yds. At 200 yds the drop is bang on 5 inches from my set up, with the load I use.
I've taken moose, bear, deer and an elk cow, on a draw tag with this handy utilitarian rifle. Groups from a bench rest set up are right around 1 moa and it stays that way right out to 300.
Even on moose, I've never been able to recover a bullet if the animal was shot around a hundred yards or less. The 338 caliber bullet is a great choice.
I stick with W748 because it works and I have a lot of it on hand.
Some of the newer powders, such as Varget would work well also as would H335. Varget, W748, H335 have similar burn rates. Magnum primers keep velocities very consistent.