I've always used a similar hat, as is shown in my picture, because I don't like sunburned ears.
You might have to put a snap on the brim to pin it up when you shoot, like Aussie style but a little further around toward the front, if you find that the brim interferes with your draw.
A baseball cap is adjustable. A brim hat is not. My head is about at the limit of "extra large" so some extra large hats fit me, and some are too small. Same thing with number sizes. Sometimes it's 7 1/2, sometimes 7 5/8. It sure would be helpful to be able to try it on before you buy it, although I'm sure 3 Rivers would take it back if it didn't fit.
I wouldn't wear any other kind of hat, but I would imagine there are 20 guys who wear baseball caps for every guy who wears a brim hat.