I haven’t seen studies specific to chicken perches, but there are a number that have been done over the years on cage birds.
All the ones I’ve read indicate a variety of shapes and sizes are best to exercise the feet and help prevent arthritic joints. The round perches that are sold with cages are ok as one option but should never be the only choice.
Debarked branches with variations in shape and size over their length are generally accepted as the “best” option, and it’s preferable to offer several made of different hardnesses as well. Moving a few inches to one side or another will then cause the feet to flex differently.
It’s probably more important to give options in wood type, size, and shape than to try to find one “best” perch.