Recoil is very subjective, and depends more on rifle than the actual cartridge IMO. My .300WinMag rifle felt about similar to a .223 in felt recoil (Boxersix and JVG can vouch), thanks to a massive Sako muzzle brake and the stock design. But round for round, out of the same rifle, the .300WinMag has more room for powder, thus bigger boom if powder charge is same for both rounds.
What optic is on the rifle? I may be buying a new rifle soon depending on how much money I want to waste.