I always put Daisy's under. She has a Swarovski crystal browband, and her forelock gets in her eyes and the wind blows it up and it tickles her ears if I leave it over. When it tickles her ears like that, she shakes like a wet dog. Ha ha.
For driving it has to be under because the blinker-holder is in the way, well it could be over but it would have to be split or pushed to one side and that would be rather strange looking. Calebs bridle has no browband, but if it did his forelock would be over, especially in summer to help shoo flies.