Hi, I earned an MPH a while ago, and I'm applying to school right now.
Are you good at math? If you want to go to MD schools, it's most likely that the only MPH courses that you will take that will count towards your crucial biology/chem/physics/math GPA are your biostats courses. If you are certain that you can rock them and you want to go to an MD school, than an MPH will do you good. The thing is, unless you are a biostats major, you won't be taking too many courses that count towards the science GPA as calculated on your MD school apps.
For DO schools, they count epidemiology courses towards calculating your science GPA. In an MPH program, you are likely to take quite a few epidemiology classes.
For me, I took 3 biostats classes for my MPH. One of them I took without the pre-requiste course, and I kinda bombed it. MD schools think that I have something like a 3.2 science GPA in grad school, so they aren't so interested. I took buckets of epidemiology classes, and I was really good at them. So, DO schools think that I have ~3.8 grad school science GPA.
I love public health, and I've built my career around it, so I can live with the consequences of having a bummer grade drag down my grad school science GPA. If you want an alternative career possibility, if you really want to make sure that public health is a component of your future career, if you looove biostats, or if DO schools are the only schools on your radar, maybe MPH is the better choice.
If your main focus is getting into med school, and you particularly want an MD school, a biomed program might serve you best. I think that those programs often help you prep for the MCAT better than an MPH program could, either through a formal MCAT prep program, or just through studying some related material and having a network of peers who are also working on their MCATs (MPH programs won't do jack for your MCATs). Biomed programs also help you establish connections with a school and its professors, making it easier to get in.
Not sure how much MD schools rank biomed programs at DO schools, though. Either way, good luck!