With max loads (for a modern levergun in 45-70) and equal weight rifles the .338 will kick a bit more than the 45-70 or 300 Win Mag (its been a few years since I shot a 45-70 much with stout loads and the only .300 Win Mag I've shot much recently weighs almost 16 lbs.). The recoil isn't near as obnoxious as a .378 Weatherby, but it's worse than most .375 H&H's that I've fired. As a-sheepdog said, the .338 Win Mag has a fairly sharp, quick recoil that punches you, the .375 H&H will actually move you around more, but its not as unpleasant.
The recoil really only bothers me when I'm shooting a lot off the bench. 15 or 20 rounds is no problem, but much more than that and accuracy starts to suffer unless I use a sissy bag or recoil reducing rest. This is really only a problem when working up a new load, I never even notice any recoil when shooting at game.