Having gone through the process of applying to Med/Psych, but ending up matching to psych, I can speak to this a little. Though of course if there's anyone in a program or an actual graduate, all the better.
The usual myth is that double boarders end up doing one or the other. From all those I've talked with, that's true, to a point. It's much easier to find a job in one or the other. On the other hand, your job opportunities are really unlimited, especially if you come from a top program. Having interviewed at Duke (great program by the way), I was very impressed. One great story was a graduate from the program having to move to ohio for her husband's work. So she sent letters to cleveland clinic and a couple other big name hospitals in the area saying "Hi. I'm coming to your area, I don't know what's available, I don't really know what I want to do, but hey, interested?" She got letters from all these places basically telling her to Absolutely come there and they would CREATE a job for her doing whatever she wanted to do.
Yeah it's that flexible.
However there's tons of drawbacks. My med school had a med-psych, and I talked to a bunch of faculty who were graduates from it. The consensus is that you get tons of job offers in practices, but that most often they're for IM practices where they just want to give you all the hardest patients, which leads pretty quickly to burn out.
The other downside is that in order to fit two specialties into 5 years, you're sacrificing HEAVILY on elective time, resulting in struggling just to keep up and feel mildly competent with two very complex fields, and not having enough time to really explore how you fit into the crossover. Also, few of the programs have really figured out how to train in the overlap, rather than just bouncing back and forth. Some are pretty good at it though, having med-psych wards, or spending a lot of time doing c/l work or primary care for psych patients (another common job for these double boarders).
But the comments before were right about money. Billing is made for one specialty or the other. So in the current system (which some are trying to change), you end up working twice as hard for less money, on the challenging patients that no one else can handle. If you're up for a challenge, there it is.
All that being said, I found it interesting because of my interest and research in mind-body medicine and psychoneuroimmunology, which I thought could work well with this double boarding. And while I really liked Davis and Duke, I ended up ranking some categorical programs higher for many reasons, and here I am. The other thing to remember is that you are an MD. Some people go into psych and choose to not use all their other medical training, but that's OPTIONAL. There's a bit of a movement now to have psychiatrists do primary care for their psych patients, because hell, so many won't go see anyone else but do trust you. A lot of residencies offer this as clinic time, including mine. Furthermore, C/L does offer some interesting overlap that you won't necessarily get if you're double boarded (more time spent focused on the crossover area), and the name itself (psychosomatics) tends to indicate that those involved can work in areas of mind-body medicine, which is where some of the research in that subspecialty is going (or so I heard on the interview trail last year. I haven't re-engaged it yet.)
Long and lengthy. The short of it is that it's a helluva lotta work, could be rewarding, could also lead to burnout, and REALLY should require intensive time to make sure it's what you want. I'd recommend doing externships at these programs.