I have trained horses in a traditional hackamore for about 18 years now and I would highly recommend them to anyone wanting to ride without a bit. Having said that though I will more than happily admit my complete ignorance about any other bitless bridles; I have never use anything other than a hackamore. I originally began using a hackamore because I was a bit na´ve and figured bits were cruel, but as I learned more, particularly about bridle training horses, I came to learn that, on the whole, most things used on a horse are only as cruel as the person using it.
The reason I like using hackamores is because if you use them in the californio style they are an entire system for training a horse which will allow you to start off with a baby that has never been touched all the way to a good going cow horse; and eventually into a full bridle, if you wanted. I have found that using a hackamore also makes you a lot more aware of what you are doing with the reins and, for me at least, a lot better on a horse in general.
There are a lot of misconceptions about them, like the idea that they are cruel, or that you can't direct rein the horse with them, these are both incorrect, as are ideas about thicker, stiffer, bosals being harsh, they are only harsh if the person using them has harsh hands and if you want to hackamore train your horse the aim is to be as soft as is humanly possible.
As for describing the mechanics of them there isn't enough room here; and besides, though the methods and the principals behind their use is consistent, the actual way you handle them, not to mention the type of bosal and mecate you use in them, will change in line with the level of refinement the horse is at in its training. But if you were interested in a life times worth of very rewarding horse riding I would totally recommend a hackamore. Reading Hackamore Reinsman
by Ed Connell is a good place to start.