I've also been debating this same issue, although for me it was neurology vs neuroscience, neuropsychology or rehabilitation sciences. Ultimately, I opted for the Master's in the field of medical science, physiology, kinesiology and neuroscience programs because there is a heavy overlap. Several of the graduate supervisors who agreed to take me are MDs or work in a hospital research lab (i.e. pediatrics, imaging, etc...). I'm not sure if it's an avenue you've considered because the research alone is clinical-based and although many researchers use animal models, quite a few use humans.

Keep in mind, if you choose to get a PhD (and post-doc) regardless if you get a MD, you will need to do research and publish often. As a result, your clinical time as a MD with patients will be limited so it will be hard to do psychotherapy. Publishing can be very difficult because after you write the manuscript, the editors often tear it to shreds. One of my friends tried to publish a paper in biochemistry. Two of the editors gave few comments, almost as though they skimmed over it, while the third editor tore his paper apart so badly he (and the other researchers) had to re-write quite a lot. Afterward they submitted it and again, it got torn to shreds. One of my professors has a PhD (pharmaceutical research for psychiatric conditions), MD (specialized in psychiatry) and MScOT (occupational therapy). He was extremely busy, even though he stopped with his occupational therapy work.

I wouldn't choose to see a clinician simply because they had both doctorates. I'd first look up their research because if it's not on human subjects, it would still be quite interesting but I'm not there to have a friendly chit-chat over a cup of tea. I would want a clinician who, ignoring other characteristics, has a flexible schedule so I don't have to book months in advance. If the person has both doctorates, chances are many people want to see them and given their already limited clinical time due to research, I'd have to jump through hoops to visit them. As great as they may be, I'd settle for someone with just a MD in that case because I know they'll have more time and energy to see their patients. If you have a PhD, you're going to need funding and that alone is a headache before you begin any research. Some people say it's a waste to get both because many people would predominantly use only one of the doctorates. Additionally, by having both, you would have a ridiculous amount of work if you tried to balance both equally. For the professor I mentioned, he currently focuses most of his effort on his PhD although he still communicates with MDs when need be.