Snaffle...most shows you can't use any bittless bridles in most shows...there's a age limit
Bitless bridles and bosals are two very different tools :) I would never use an actual bitless bridle, because of the pressure they can exert on really sensitive parts of the horses head, but I do like bosals. I don't like that the bitless ones put pressure under the chin, just not my cup of tea.
Interesting tidbit by Dr. Hilary Clayton (a really smart lady, love her books!) in this article: Bitless or Not, It
I liked her point that taking away a bit doesn't always mean you're being 'nicer', as bitless bridles can create more pressure than a regular noseband will.
That being said: a bit in the wrong hands, a bosal in the wrong hands, or a bitless bridle in the wrong hands can ALL be harsh- please don't think I'm saying snaffles and bosals are the only kind thing to use on your horse; nothing replaces proper fundamental training which teaches the horse to move from back to front. The horses headwear becomes much less important if they are trained this way from the get go.
For my purposes, bosals and snaffles serve me well. I feel like I can give direct, specific feedback to the animal with either. If I were to choose though, I do like using bosals as long as is legal to show with them.