Just as a note, one is called to live the gospel life and call according to one’s state in life. Thus, whether one is called to lay affiliation with the Franciscans or the Dominicans, one must live that charism according to one’s state in life.
So I had to chuckle when I saw your post which said, “I can’t be preaching at my patients all day.” Well, that’s true, but it’s also true that you can’t give up all your stuff and live like a hobo. Giving up all your stuff is textbook “Franciscan” living, just as preaching like the dickens is textbook “Dominican” charism-- but lay affiliates are called to the charisms of preaching and poverty in the Franciscan and Dominican lay orders according to a manner which befits their state in life.
(I would add, of course, that poverty and preaching are characteristics of both orders. I can’t imagine St. Anthony not preaching any more than I can imagine St. Dominic not poor-- and if you read a good history of the early order, you’ll see that the early Dominicans were especially zealous for poverty, because St. Dominic was extremely zealous for it. Likewise, St. Bonaventure’s intellect equaled St. Thomas’s-- but let us not forget the zeal for the poor which the humble lay brother, St. Martin de Porres had… or indeed, for justice for the lowly which Bartolomeo de las Casas had. There’s a lot of overlap-- the orders are brothers to each other.)
Instead, a poster above I think gave some sound advice. The Franciscan charism focuses more on the corporal works of mercy. It tends to help the body. The Dominican charism tends to focus more on the spiritual works of mercy. It focuses more on the soul.
As a doctor, you of course treat patients according to their bodies, and not their souls. This might mean that you’d fit in better with the Franciscans, even though you are a very intelligent and intellectual person. Your ministry is to their bodies.
On the other hand, as a doctor you are in the center of very serious issues in our contemporary society: medical ethics. Medical experts who are good Catholics and also experts in orthodox Catholic ethics are incredibly necessary in our Church today. It is a central battleground. This would tend to be a more Dominican sort of charism. It aims more directly at the soul.
My sympathies, of course, are with the Dominicans.
But remember this too: just as the human being is soul and body, so too our relationship with any order must be soul and body. You need to like not only the abstract: the charism in theory, and the spirituality of the founders and saints, but also the concrete, the body if you will: the actual people to whom you will be brothers and sisters, and with whom you must become friends. That’s why I say go and visit both. You might just click with one rather than with other. You need to know them in the flesh before you can decide.