I'm one of those that use tree branches. With mine, the thickness of the tree branch is not nearly as important as being near the window. I am convinced either one will work, mainly because people do it both ways and both ways work. As Ddawn said, you are not in a climate where them sleeping on their feet should be a concern. Even on the narrowest of my tree branches where their feet are wrapped around pretty good, their feet are pretty well covered by their feathers anyway when they squat down.
Something I did not see anyone mention. Whichever way you position them, round off the corners of the 2x4's. This is more comfortable to them when their feet wrap around the roost and it gets rid of splinters.