humboldt
Humboldts are used almost exclusively in the Western US and Canada.
The primary advantage of the humboldt is that you get a squared off butt log for the mill. The bottom part of the face is meant to come out of the butt swell. That is a part of the log where most of the time, the logger wants to avoid. Cause the swell is difficult to work with on even simple things like loading a log truck. If you're around many of these bigger trees it gets fairly obvious why.
Humboldts are more difficult to cut and not really necessary on straighter bottom log timber.
Convention faces are the easiest. In some instances on straighter bottom logs they allow you to get the most wood to the mill, as you can cut lower with them than either a humboldt or open face. In the small world of fire fighting I come from the conventional is the most popular as it allows the cutter to look up the most. A truly important item when dealing with snags and recently burned trees.
Open face are the most difficult, but do have some real advantages. But that is another thread.