Since I am an independent project management consultant I can only answer from that perspective:
Most: The variety of clients and challenges. I often have taken on "failed" projects as the turnaround expert.
Least: Long hours often away from home and sometimes not billable, even as an independent.
Middle Least: Difficult clients who don't disclose the full extent of the problem up front.
Challenging? Yes, nothing more challenging than PM work especially as an independent.
Learning Opportunities: Absolutely
Advancement: No, not as an independent. I suspect as an employee the answer is much different and even this will depend on whether you are within a consulting firm or industry.
Love PM work as an independent, love the challenge and most of the time my clients even the difficult ones. Love solving problems especially the "off the rails" projects. Even like the travel.