I believe my chookies can roost more comfortably on square roosts--especially because sometimes they come directly from a rainy, wet yard and jump onto the roost with damp feet. Those roosts tend to get a bit slippery at times.
For me, its about what my chickens prefer. They have been usuing their nest boxes for the past 4 months. I had 2x4's and 1x2's and an assortment of other things trying to find what they likes. Several days ago I used the metal closet rod hangers and wooden closet rods- about 2in in diameter. The first night, they hopped right up there and have been sleeping on them ever since.
Her's why I ask....... When I kept the chickens in the barn, they would roost on the top 2 rails of the metal horse panels between stalls. I was getting mad because we filled the barn with other animals, dogs, goats, chickens, ducks, a goose........... and there was no room for the horses - whom we built the barn for! So now we are building a new chicken coop away from the barn and I have all shapes of wood available and don't want the chickens to go back to the barn to roost on the round rails. (I'll have to lock them up for a few days in their new home)
Chickens like humans will have their preferences, but they usually prefer high. So what ever they can get to that is highest will be their favorite. That said, if you make them a roost spot, a flat 2x4, with the big side flat for them to sit on is best. Unlike many other birds like tree dwelling types, they don't grasp while asleep. In cooler climates, flat feet also prevent frostbit toes.
Try putting a bird on your arm. When it relaxes while sitting, you'll lose the feeling of feet and instead feel the keel on your arm.
I've got 1" round dowels, 3" (flat) boards and 4" (flat) boards available for them to roost, and they all choose the flat boards over the dowels when they go to sleep. They don't seem to care whether they're on the 3" or 4", but they definitely do not like the dowels for sleeping. Having said that, I did see one of my girls trying to roost on our clothesline the other day. She was doing quite the trapeeze act, I can tell you!
I tried 2x4ʻs with the wide side up, but they kept pooping on the boards. With the narrow side up, they pooped behind the roost board. I live in a warm climate, so cold feet arenʻt a problem, but sanitation can be.