So, my MA was in medieval history and not medieval studies. Here is the difference - to be a medieval studies program, the school has to have the tools to train you in paleography, latin, medieval historiography, etc. An MA in medieval history (which is what I did) allows you to take historiography classes on the medieval/early modern period, and produce a thesis on a medieval topic. I focused on late medieval Italy and worked with French and Italian.
As far as the question of negatives - it will be much harder to get a job with a medieval studies PhD. Not impossible, but very hard. If you get a degree in history, you have a little wider options. No matter what you do, my advice would be to a) do what makes you happy and b) make sure that your project is broad enough a topic to help with the job market.