I haven't any experience with a 37, but I own the rest of them (except a Mossberg, but I've shot my brother's).
The older designs in the group with the tilting bolts are indisputably smoother. That said, part of pump practicality is economy. I think the 870 best bridges the gap between elegance & practicality. There may be some stamped mousetrap mechanisms on the inside, but a TB or TC with high grade wood & deep blue is still eye-catching.
It always irks me when I see the Mossberg associated directly with the 31. I'd say the Mossberg's parents are the High Standard and the 870. Now, the High Standard - THAT's largely a cheapened 31.