I know the Freiberg compass well as I am using it, but the Breithaupt seems to me similar in shape. Is there any difference in use or only in the companies?
there is almost no difference except in the stabilizing and damping effect on the needle of the compass, which is less well done in the Freiberg-type. You need more time for the measurement using the Freiberg-type.
As mentioned above, both devices are build as a stratum compass and you measure the attitude of planes or lineations in one measurement procedure (2-circle measurement of strike on compass rose and dip circle in the hinge of the Compass lid). This is very convenient if you measure lots of data in tiny spots and use computer software for analysis because you record data already in computer-friendly dip annotation rather than azimuth-dip annotation.
Freiberg and Breithaupt are two different brands with the Freiberg version being less expensive (well-liked by students) and the Breithaupt version is the high-spec version you would consider as a structural geologist depending on your tool under all working conditions, adverse weather and extensive field expeditions.
As mentioned above the Breithaupt Compass has very well designed features like the magnetic needle dampening system, a spirit level with mirror and a lateral release button to allow you to measure even overhead with one hand if required.
Bottomline, the price of the Breithaupt is several times that of the Freiberg version and the choice mainly depends on your economic restrictions. If you measure a lot, year on year as part of your profession, the Breithaupt compass will allow you to measure with high reliability and efficiency and it will never fail.
I have inherited mine from my MSc supervisor. He used it already for 25 years all around the world, I use it 25 more years since and I am extremly happy with it. Our students use frequently the Freiberg version for their fieldwork and they work well and do a reliable job but they may be less efficient and less reliable under rough conditions.