The regular style is the most affordable and is rounded on the sides.
The boxed eave and vertical styles look exactly the same except the roof sheeting on the boxed runs length wise and on the vertical roof style the sheeting runs up and down allowing snow to slide off on the vertical roof style.
The vertical roof style is the strongest style. In order to have the roof sheeting go up and down on the vertical style there are metal cross braces that the roof sheeting is attached to which makes the vertical style even stronger, but due to the materials and time it is the most expensive of the three styles.