Yes a pump shotgun will have more felt recoil than a semi auto, what makes a big difference is the type of loads you’re shooting alot of the time. How you shoulder the gun is a big factor, in recoil mitigation. A good gel recoil pad is also a big help in taming felt recoil. 870’s are heavy enough that they help to soak up some felt recoil, a light break action shotgun and a stout load can rattle your teeth. Where the same stout load in a heavier pump gun won’t be as punishing.
Regular 2 3/4” trap/field loads are pretty tame, start there and work your way up to some stouter loads and you’ll be fine. When I bought my wife a 12g she was a bit hesitant the first time she shot it, she was expecting the worst so I started her with #7.5 2 3/4” field loads. After a few of those she fired off some 2 3/4” 00buck and then some 1oz slugs without any problems.