To add to this discussion. There is an article in the October edition of Sport Aviation on page 34. It is Charlie Precourt's column titled "Demonstrating Ingenuity". The core of the article discusses the pros/cons of a squared vs. rounded traffic pattern. The interesting part is a reader providing data from his aircraft while flying both patterns. The data on AOA and Bank Angle is very interesting, it shows that the AOA increases more that you may think when making square turns from downwind to base and then to final.
It is a good read and shows that AOA display shows your margin of safety, regardless of other factors you may feel are giving you good information (i.e. airspeed, but feel, deck angle)

Ralph