So I looked it up. Turns out "tombstone" refers to the shape of the metal gizmos that form the slots. They look like a circle of old-time tombstones. Tombstone feeders with their rounded shoulders are better for horses because the smooth shape doesn't catch and pull out mane hair. Horses slip their heads through and eat--though I would worry that my dominant mare would come around and chase the other two, and they could get hurt if they were caught with their heads through the slot.
My guess is that they would worry too, and would adopt a snatch, pull out, and munch outside the feeder style of eating. That's why a basket-style feeder would be better for a herd with bossy horses in it. Horses don't put their head into the basket at all. They pull hay through, as they do from a manger or hay net.
Right now though, my horses are eating hay from piles on the snow, and getting lots of exercise walking (or being chased) from pile to pile. It's the most natural way, and they sure look pretty out there.