I would say that you should look carefully at the specs and really think about how
you are going to use the camera. I am no expert, but I can tell you for sure that a bigger
camera is easier to hold steady and that the controls are easier to use. I would not exclude the FH-25 from consideration.
So if you are going to achieve the critical alignments, you really need a tripod. I would say this is true even if you have a helper operating the camera. I have read that the parallax phenomenon is minimized by placing the camera farther away and using the zoom feature. On the other hand, Brian whipped out his FH-20 and shot me from behind to show me a specific thing with my clubface at the top.
Unclear whether the FC-100 and/or the FH-100 have a mount for a tripod. If you are going to use camera in the role of instructor, then logically you should use the cameras they use.
You need to use Shutter Priority mode. The FC-100 lists only AE Program, whereas the
FH-100 shows Shutter Priority available.
The size of the LCD matters, FC-100 is 2.7, FH-100 is 3.0.
Optical Zoom - Smaller cameras are 10X, FH-25 is 20X
Batteries - FC-100 uses a Lithium Ion. You may need to buy an extra.
FH-25 uses common batteries.
If portability is your issue, then from the specs it appears that the FH-100 has the better specs.