A 375 isn't a big deal. Just get a decent recoil pad, and if possible, shoot it from a standing rest. Hunched over a bench, leaning into the rifle, and you'll notice for sure. My 375 isn't any worse than a buddy's light-weight, 7lbs 30-06.
Slugs, well, that's a whole different game. 107ft/lbs of recoil for my last bunch had me dazed and confused and bruised and full of adrenaline. Made for quite the afternoon. After shooting those things the 375 is nothing.
So long story short, it's not bad, you get used to it.