338 edge has much more recoil. I can vouch for this in a true apples to apples comparison. I had a 300 RUM which was later bored out to 338. Same rifle just a bigger bore. I noticed right off the bat that it hit me much harder even with just 225 grain pills. 300 grain pills are unbearable in a 10# rifle. Even with a muzzle break.
When you gotta ask that type of question you'd better stay away from both...NEITHER of them are comfortable to me off the bench..after 3 shots I'm done and want nothing to do with either.. maybe you better stick with a 300WM, heck it'll touch out to as far as you'd like.
I find both a pleasure to shoot but you'll never catch me pulling the trigger without a proper brake on either!!! Technically the 338 has more recoil, in same weight class bullets the 338 can utilize more powder or you can launch heavier bullets with it so it's the winner. The last 338 RUM I braked was very comfortable to shoot with 300gr bullets from the bench and it was a bare factory Rem that could not have weight 8 lbs, a good brake, well installed is worth it's weight in gold on any RUM IMO!!
I'm sold on the Muscle Brake on this latest Mark V 338 Lapua build. In the prone on a bipod/rear bag, I swear the felt recoil is less than a unbraked 7mm Rem Mag pushing 180 Hybrids at 3000. Off hand, the rifle is brisk though.
So I think "felt" recoil is very reliant on many factors (i.e. shooting position, stock design, recoil pad, muzzle brake/type, etc)....be best to drive before you buy if you can...and if you find a setup you like, to build based off that experience.
I actually find the recoil in my 300 RUM to be more harsh with 180g than 200g bullets. The recoil with the 180s is 'snappier'...harder on my shoulder. I'm about 190 lbs and my RUM doesn't have a brake on it. I shot 14 rounds at the range last night off of the bench and I'm slightly sore today. On days when I go through 20+ rounds, I can definitely feel it the next day (or two).
I've thought about putting on a brake, but I'm concerned about ruining my hunting partners' hearing. So, I suck it up at the range. Never shoot more than a couple of rounds when out hunting, so the recoil is never an issue out there.
My 300 rum started out as a factory sendero which had the heavy fluted barrel I once shot several rounds from the prone position (no break) and I could definately feel it on the top of my sholder. I now have a DE brake on it and it kicks like a .308 or .243 . I could shoot round after round prone or from a bench.