I'm pretty sure that you can't show in a bitless bridle--you'll have to check the rules. Hackamores have to be used carefully--they put a lot of pressure on a horse's face. Hackamores can stop horses effectively, but they aren't great for turning a misbehaving a horse--no bitless bridle is, in my opinion. I posted a lot about this recently in a halter-riding thread, so I won't repeat--just hit my profile, and look back through my posts. One nice thing about a bit, even a snaffle, is that you have control over their nose, and thus their head, and thus their body. I'm not anti-bitless, I've been giving a lot of thought to switching Arrow over--but he's well trained and not prone to lots of misbehavior, either.