Preventers and boom brakes serve similar functions but do it quite differently.
A boom brake is designed to slow the boom, if the boat gybes. It does not stop the boom from crossing over the centerline, but is designed to slow the speed at which it can do it... removing most of the risk of an accidental gybe. A common brand of a boom brake is the dutchman boom brake, which you can see here
A preventer is usually a line that is run forward to a padeye or chainplate, and prevents the boom from swinging across the boat. Here is a diagram of a preventer setup on San Juan 23.
The main difference between a boom brake and a preventer is that the preventer needs to be manually released to allow the boom to gybe—the boom brake does not.
There are a few risks to using a preventer which a boom brake seems to avoid.
First, there is a greater risk of breaking the boom with a preventer, rather than a boom brake, since the preventer has far less give than the boom brake, which allows movement of the boom.
Second, there is the risk in the case of a broach of the main backing and filling on the wrong side of the boat. This can allow the main to pin the boat down. Not exactly an ideal situation.
BTW, I have a Dutchman Boom Brake on my boat.