What are the advantages and disadvantages of each choice for ships doctor?

If you pick Doctor Chakwas you find out her first name and you will share another bottle of Serrice Ice Brandy (if you shared one in ME2).

If you pick Doctor Michel, Doctor Chakwas will stay with Hackett in Alliance R&D and awards you a War Asset (I received +10). Her background specifically mentions alien physiology so I don't know how that might play out either in helping your team or through some unknown thread in R&D. She has more dialogue than Chakwas, including info about the implants inside Shepard(Lazarus Project). You also might get some more info on Banes(ME1), if the rumor that Banes will be back in Mass Effect 3 is correct.

The Normandy Doctor sends you on a quest. If it's Dr. Chakwas, the reward is a Medi-Gel efficiency upgrade, if it's Michel it's Medi-Gel capacity.