The pros and cons will vary depending on the SP and the agency. So, I cannot really give a general answer. But I can answer it from my perspective and experience.
When I started in the business, working with an agency was the most convenient for me: they were providing me with an initial client base and the basics I needed to start (website, pics, advertisement) without having to invest time or money in it, and with a support system to rely on while I learned the particularities of the industry. At the time, I didn't feel that my schedule allowed me the time to do my own communication and bookings, so contracting an agency to do it for me was also more convenient for me. After a while working with an outcall only agency, I wanted to do incalls mostly (more convenient for my schedule as outcalls tend to be mostly in the evenings and incalls during daytime), and the agency I moved with was providing me with a space to work from.
After a little more than a year in the business, I decided to go indy for a few reasons: the primary one was that I wanted to be in full control of my business, my image, and my clientele. The costs of contracting an agency weren't worth anymore what I was getting out of it, and I had the opportunity to share a work space with some good friends which was not only cheaper but also more fun and convenient for me than working from the agency space.
I am really happy that I made the decision to work indy, and I enjoy my work even more now than I did when I was working with agencies. But a large part of my success and happiness with my indy business comes from the support system I have around me: I have a fantastic group of women surrounding me who I work with, share a space with, and can count on for support. So, from my perspective, I now have the best of both world: I have complete control over my business while being surrounded with great friends who I can share resources with and rely on for support.
I think that in most cases (and at least in my experience), the SP contact the agency, not the other way around.