The 2 psychiatrists that I know with MBAs have somewhat divergent career paths. One of them initially practiced hospital-based community psychiatry with some administrative responsibilities, then moved into the area of managed care mental health carve outs, working as medical director of a company's regional office. He did no clinical care, but did direct a lot of QA/QI measures and interacted directly with psych providers to give them feedback on the QA/QI (e.g. "why are 1/3 of your patients on a regimen consisting of Lamictal 50, Abilify 5, Seroquel 100, and Zoloft 50?") which he felt was going a long way towards improving overall quality of care for an employed and insured population. He transitioned to working for the non-profit mental health carve-out company covering a large number of managed medicaid programs, so has the ability to compare the quality of services provided between commercial for-profit insurance and non-profit medicaid.
The other person, took a job in an academic center and then used his administrative abilities to quickly move up the ranks, until he became a big-wig in the overall hospital administration. I'm not sure that he practiced psychiatry any longer, but he did talk extensively about the management style of psychiatrists being more a relational approach and how this helped him navigate some of the politics of the academic med center.
Hope that helps!
MBK2003