At our veterinary practice, we made a simple twitch using an axe handle with a hole drilled through the end, and a nylon rope threaded through and knotted. There are many other similar designs.
The most common design is the “humane twitch”. The problem with this device is the inability to change the degree of pressure on the lip and the difficulty in releasing it if it is tied closed. Chain twitches work fine but are more likely to bind and pinch the lip. They are also more harsh than a rope twitch. Used improperly they can badly bruise the lip.
A properly applied twitch, used on the right horse, is a very useful mode of restraint. It is not inherently cruel. The humanity of the device is in the hands of the operator. The twitch has been shown to cause an endorphin release in the horse. Endorphins are natural pain killers which exert a calming effect on the horse. Proper application of a twitch allows some (not all) procedures to be performed more easily and safely.
It is important to know that there are horses that tolerate twitches well, but there are those that respond adversely. Used on the wrong horse, application of a twitch can be very dangerous. It is how the twitch is used and the events that lead up to its use that determine whether it is a suitable form of restraint. In my practice, an effort is made to perform most procedures without a twitch, prior to its use.