(I originally wrote this as an answer for Quora)
They are VERY different jobs and an individual is probably going to be a lot better at one of them than the other.
My first job out of college was being a production artist for a small (about 7 people) design agency. I soon worked my way up to designer and soon after, I led the team as Creative Director.
And shortly thereafter I decided to go out on my own…
Managing the team was not enjoyable for me as I don’t like being held accountable for other’s behavior (making sure people are treated equally, hitting deadlines, calling off work…).
I also have never been a fan of paperwork. There’s a ton of paperwork to do as manager of a team — quotes, proposals, tax stuff, training materials, marketing plans.
And there’s being the project manager. That takes a lot of organization skill. I was very good at it, but I didn’t care for that responsibility as much as designing cool things.
Finally… you have to know much more about marketing if you’re heading a design team. That’s because you will often be the liaison and spokesperson for your team — engaging with your clients and collaborating on shaping the project that is to be designed.
In the end, I decided that if I had to do all those things anyway, that I’d just prefer to do them on my own terms, and the teams that I use on given projects are virtual, so that end of things are more manageable.
Managing a design team takes leadership and organizational skills and I’d imagine a lot of people may find that they actually enjoy and excel at it more than being a designer as they’re completely opposite skillsets. And vice versa.