I wish I knew a physician with an MPH that I could discuss my options with.
I guess this applies to me, although I am sure there are others here more advanced in their training who can give a broader perspective.
I did a 2-year epi MPH before med school. I'm currently a first year resident in internal medicine, a specialty with a fair number of MPHs. I've primarily used my MPH background for research.
Its been a while, but I thought most if not all of the med schools I looked at were more than happy to let students take a leave of absence if you had a good reason that would add to your career. And I also have this vague idea that the respectable med schools would be happy to let you do your MPH at whatever institution would be the best fit for you. If nothing else it would help you match into a stronger residency and make them look better. I would also think that if you were strong enough to get into an MD or DO program, you would be able to get into a good MPH program as well. I seem to remember getting the sense that SPH's were eager to train MDs/DOs who had a serious interest in public health.
I don't know much about online programs, but I would be wary of them. I had a med school classmate who did a program through Hopkins that had a significant online component, although she still had to travel to Baltimore on a regular basis. She seemed happy with it and I'm sure it worked out great for her.
I wouldn't recommend trying to do an MPH while doing med school full time. It would be theoretically possible during years 1-2 when you largely control your own schedule (wake up, study, eat, go to lecture, study, go to lab, study, eat, study, shower, study, talk to significant other, study...). It would be physically impossible during much if not all of the med school years 3-4.
If you were going to take time off, probably 1-2 years, you would have to think about when. Probably not between years 1-2, as the basic science probably goes better as a single 2-year block. Many people would elect to do their MPH time between years 2-3 as that is a natural break between classroom work and clinical work. And an arguement can be made for between years 3-4, after you have a year of clinical experience and maybe have a better idea what you want to do clinically. Many, probably most, people change their residency choice during year 3.
I think doing an MPH between med school and residency is less popular, if for no reason than it would disrupt everything your med school would do to help you go through the match. I know somebody who did it and it worked out great, though. I also think it makes less sense for most people, as your MPH experiences might alter where you want to do your residency, and in what.
You certainly can do an MPH while in residency, but you would have to take time off. Again, I would think most good residencies would be happy to help you arrange for an MPH during your training although getting funded to do it might be tricky unless it's part of a specific training or fellowship (i.e.-preventive medicine fellowships usually let you do an MPH and pay you at the same time, IIRC). You could also do it while practicing, but the time pressures seem just as bad (perhaps more control over your schedule, but usually more family commitments and less desire to be a student again).
Unless you have some extensive public health experiences, I suspect it's impossible to know now exactly what you want to do and therefore impossible to know if NHS vs EIS would be better. I've known people who did both, and they are now in very different areas. It seems a little like asking if you should do your residency in internal medicine or surgery...at least do your third year of med school first!
The benefit of an MPP vs MPH would completely depend on what you want to do. I've never heard anybody suggest that one was better than the other overall, although I'm sure for some specific things there are pluses and minuses. I guess more people know about an MPH whereas they would have to think about what an MPP was. It would also depend on the MPH major - I think my MPH (in epi) was very different than my friends MPH (in public health nutrition), even though we went to the same school.
Well, there's my $0.02. I hope it was at least a little helpful.
