Could you be more specific? The garrote you describe (wooden chair with neck bolt) wasn’t a single thing, it was several different mechanisms. The chair and some kind of manipulation of the neck were common to all, but the actual operation and mode of death could vary.

For example, it could be as simple as a metal band or rope placed around the neck, which was tightened to produce death by strangulation. The method of tightening could be as simple as the executioner pulling the ends of the rope with his hands, or he could slip a stick between neck and rope and tighten it by twisting the stick, or in case of a metal band by tightening a screw on the band.

Then there was the Catalan garrote, which held a wheel-shaped blade attached to the neck band, and tightening the band caused the blade to sever the spinal cord. This was a different mode of death than strangulation.

There was another type of garrote which consisted of two metal bands placed adjacent to each other around the neck. One band was stationary while the other could be moved by turning a wheel, and the goal was to kill by dislocating the neck. This would be similar to death by hanging, except that it was less messy and there was no danger of tearing the head off, or leaving a half-alive victim dangling at the end of the rope. You just kept on turning the screw until the neck snapped.

So depending on what you’re talking about, the chair plus neck bolt could kill by strangulation, by severing the spinal cord, or by dislocating the neck. All of these things could be done quickly or slowly, depending on how fast the executioner turned the screw or twisted the stick.

If you define "humane" as something that quickly produces unconsciousness, then none of these methods were particularly humane. Probably, strangulation could be considered the most humane among them, if done properly. Medically speaking, 10 seconds of brain ischemia produces unconsciousness, but it requires an executioner who knows what he’s doing and who deliberately wants to kill as quickly as possible. None of the other methods (turning a screw to sever the spinal cord or to dislocate the neck) could be done in 10 seconds, and the intervening period would be very painful.

There are many variables in physiology and people are all different, so it’s not possible to guarantee that any given person will die just as quickly as another. But if you are speaking relatively, then none of these garroting methods offered a death as quick as hanging or a firing squad. A proper hanging dislocates the neck in milliseconds, after which the victim feels nothing. A well-trained firing squad puts several heavy caliber bullets into the body pretty much instantly. Even if they fail to hit a vital organ, the shock of the impact will induce unconsciousness almost immediately. Of course, it’s possible to bungle a hanging. If the drop is too short to snap the neck, you could leave the victim to dangle for a few minutes as he slowly asphyxiates. Or a firing squad could miss and leave just a couple of non-lethal wounds and have the victim slowly bleed to death. Human intention and human error are always relevant.

If you provide some details about what type of garroting you wish to know about, and possibly some historical reference to when/where it was used, someone might give you a more detailed answer.