Not much more to add. Why pick one over another?
Do you mean a fork equatorial mount or a fork altazimuth? They're the same mount, but one is tilted over so the "azimuth" axis points at the Pole.
The main down point of German equatorials is that they require a counterweight nearly equal to the weight of the telescope. Not only does the mount itself have to carry twice the weight, but the owner of the mount has to transport twice the weight. A fork equatorial doesn't need a counterweight, but is inherently unstable, with a lot of weight hanging off the tripod in one direction. To minimize vibration, this requires that the fork arms be beefed which increases the overall weight.
My favourite mounts are all altazimuth, either Dobsonians or motorized altazimuth fork mounts. These are inherently stable because the centre of mass is right over the tripod. Their major drawback is that they can't be used for photography because of field rotation. Their main advantage is that they don't need polar alignment.
All mounts have a zone in the sky where they can't be controlled well. With Dobs and upright fork mounts, that's called "Dobson's hole" right overhead within about 15° of the zenith. With any equatorial mount, the problem zone is within about 15° of the pole. For equatorials have a larger problem zone because the eyepiece becomes inaccessible when under the mount.
So they all have pluses and minuses. In a permanent observatory, a German equatorial is ideal. The extra weight doesn't matter and operation and accessibility is excellent. For sheer portability, a Dobsonian in tops. One arrangement that worked well for me for several years was a large Dobsonian on an equatorial platform. This had the ease of movement of the Dob combined with tracking for over an hour without resetting.