We have a good comparison with a country that is similar to the US in lots of important ways, but lacks a constitution (the UK).

My personal view is that this lack of a line in the sand in the UK makes it easier to trample on people's rights for bureaucratic convenience, basically. The English culture has fairly good totalitarian antibodies, and this is what makes it work.

edit: Lately I started thinking that maybe it's all culture in the end, and things like having a constitution or a parlamentary system vs something else means very little once culture is fixed. Perhaps there are (culture-specific) society traps to avoid (hi Germany!), but aside from that there is probably a lot of robustness to organization type.