More to the OP, if you are thinking from a strict marketability perspective in terms of getting into pain, it's Gas>PMR>Neuro>>Psych. That said, competitiveness is way down and recent trends seem to support psychs that want to go into it, able to do so. Get as much needle time as you can as a med student, as an intern, and in electives. Go to a program with elective time and with a good relationship between psych and pain.
From what's going to benefit patients the most, I think Gas is inferior to the other three fields. Functional anatomy and deficits, looking at scans all day, understanding the nervous system peculiarities, and the ability to both understand psychiatric contributions and deliver effective psychosocial intervention seem pretty important.
To my mind, it's a tossup between PM&R and Psych in terms of which will help patients the most. PM&R docs have the functional anatomy knowledge, the familiarity with neuromusculoskeletal functioning as a whole, and an understanding of the physical process (including brain) that leads to pain. The ability to detect and refer or intervene for compromised movement patterns, identification of pathologic compensatory drives, or reversible (through PT or surgery) deficits is huge. Their training basically also revolves around 'making the best of a bad situation' which is I think inherently a good mindset to develop in this population.
As for psych. Well, we know that Trauma, Depression, Anxiety all lead to increased perception and sensation of pain through various psychogenic, forebrain, limbic, and hypothalamic processes. We also know that personality factors greatly change the experience of pain. And, psych will give you a broader range of training in various psychotherapeutic interventions that are quite helpful for pain. Things like mindfulness to decrease pain catastrophization and limit secondary panic/pain responses (Bodhidharma's Second Arrow...or the Hick's Second Fishhook) and to enable one to still have a pleasant time despite the pain. Acceptance and committment to work through feelings of loss and frustration associated with a permanent state of pain. Behavioral Activation to keep moving, stick to PT, and ensure counterbalancing positive stimuli remain present. Motivational Enhancement Therapy for reinforcement of all of the above. This is in addition to being an MD who can therefore discuss their diagnoses with them with some degree of facility. Not to mention psychiatric meds with pain benefits (gabapentin, cymbalta, effexor
I've had quite a few patients who ended up in psych clinic after pain clinic fired them. One of the most frustrating things about this population is wishing 'we' (meaning psych) could've gotten to them earlier. They've mostly tended to respond very well to psychiatric intervention.
A perfect pathway into pain would be a PM&R/psych combined residency followed by pain fellowship.