If the rifle weighs 8.5-9 lbs and the stock is a good design with a good recoil pad the recoil is not objectionable. If you purchase a SPS "tupperware" stocked version it will kick the boogers out of you. Those stocks are just plain painful with the larger cartridges. The 338 RUM with its heavier bullets should recoil with more ft/lb if all other factors are the same.
If you handload you can work up your tolerance to the recoil by shooting lighter 150, 165 gr bullets or load it down a bit with the bullet of your choice.
My 300 RUM weighs 9 lbs. It is in a McMillan hunter stock, has a decelerator recoil pad. Recoil is not bad with this package and it shoots the 200 gr accubond at 3200 fps.
Here is a recoil calculator to help you get a clue of what you will experience vs the 338 RUM you shot.