The biggest issue with a square is it takes up more of the room than the rectangle or L shape would. I know that sounds daft but think of it as putting in the equivalent of a sofa and a bench. The bench fits against the wall, whereas the sofa juts further into the room. It worked for me because I had two sofas (well, it was a rented place, and it came with two sofas) so two walls got a sofa and the back wall got bookcases, and their cage went on the floor in the middle of the room. They were well adjusted (as can be anyway) to being in the room like that so it wasn't a massive issue for them, they still went bonkers when they felt like it even if strange people were in the room.
It can also be harder to clean out, depending on your access to the sides. Ideally you'd want to be able to get at at least 3 - it's a lot harder to reach across 4ft than to reach across 2ft.