Good question.

I voted for 'fixed braces, no headgear' because, on balance, it would probably be a better overall experience for the wearer .

Fixed braces score maximum points for being permanent and giving a nice tactile feeling but not quite as high for visibility or embarrassment factor (although it is quite hard to effectively hide train tracks).

Headgear obviously scores maximum points for visibility and embarrassment. However, it lacks the tactile satisfaction of fixed braces, and, in the real world, it's not permanent. I suspect the experience of wearing headgear with bare teeth might be a bit boring compared to having brackets on every tooth. There is also a much greater risk of non-compliance unless you are the 'victim' of one of the stories on this site or a Braced Life model