I guess that depends on your personal goals and interests as a clinician. Think of it this way: Medicine is about the TREATMENT of SICK INDIVIDUALS. Public Health is about PREVENTION of disease in HEALTHY POPULATIONS. The principles and practices of a public health would, for example, parallel the goals of a primary care physician who would have the opportunity to address other social and environmental factors that affect health, versus simply treating problems medically.
Having said that, public health physicians can do anything that a MD without an MPH can do. Many work in government (i.e. CDC, HRSA), some work for or run non-profits, or just work in communities. But it's not about where the physician works or even about having a degree in public health, but about how clinicians intergrate public health practice into their own work. Otherwise, the MPH is just another set of letters behind their name.
Hope this helps,
H&T, Person with MPH
EDIT: I might also argue the same for the MBA degree.