I work in an FQHC so I can give you that aspect. There is no ownership aspect in these practices - most will have a dental director that oversees the running of the dental clinic, but financially speaking they receive most of their money from federal funding and grants. This makes them generally harder to "go out of business" than a private practice.
As far as procedure mix goes, this can vary greatly from one FQHC to another. For example, in some states medicaid doesn't cover dentures or crowns, so these procedures would be less frequent in those clinics. I live in Wisconsin, our medicaid program covers a wide variety of procedures. I do operative, oral surgery, fixed prosth, removable prosth, and endo. Not a lot of implant candidates coming through our door unfortunately.
For me, I have no interest in running my own practice. In my position now, its 8-5 and when I'm not there, I'm not thinking about it. There's minimal stress compared to some of my buddies who are now owning their own private practice and dealing with hiring/firing, insurance, billing, etc. Another big perk of FQHCs is loan repayment. I think at the least its a great stepping stone to ptivate practice - gives you time to build up speed and confidence before going off on your own