By the time I had read this answer to this question, I had already recruited Dr. Chakwas to serve on the Normandy. I now realize that there's a better benefit to recruiting Dr. Michel instead. Is there any way to switch which doctor I have recruited?
Shepard can choose either Dr. Chakwas or Dr. Michel as the Normandy's Chief Medical Officer. If Chakwas is chosen, she can again be found in the medical bay of the Normandy SR-2.
If Shepard tells Dr. Chakwas to stay on the Citadel, she will continue to work, and provide assets for the war.
This is an exclusive decision in that you can't pick both and I have found no way of switching doctors; Chakwas becomes a war asset if you don't pick her. I don't personally know if the other doctor becomes an asset in the same way or not.