Ryan:
Good design is all about considering site factors in your design (soils, drainage, vegetation, contour, etc.) and making the best of them. Whether a course is public or private is relatively minor by comparison, so any good designer ought to be able to consider that, too, from one project to the next.
However, there IS a pretty standard career arc in this business. When you are young and unproven, most of the work comes from public courses. Once you're a name and the fees go up, private courses and development courses become the bulk of the work, because the smaller clients don't think they can afford you. There are exceptions -- modest private clubs at the one end, very expensive public or municipal courses on the other -- but they're the exceptions.