They are pretty much the same. Similarly, one can get an M.S. or an M.P.H. in most programs that are accredited. The difference is that the MS and the PhD are more geared toward research and academics. The MPH, and to some degree the DrPH, is geared toward application of public health principles. If you were interested in government or non-profit work, having one of the "PH" degrees might be slightly advantageous. I've heard that in some circles, having the "PH" degree opens doors (kind of like being a card-carrying public health professional). For instance, even some faculty positions I've seen in preventive or community medicine say "either MD/MPH, Ph.D. or equivalent". But, for nearly all cases, the same doors would be open with the PhD and the DrPH. In academic circles, you may find those who emphasize research favoring the PhD and those who favor academic "service" favoring the DrPH.
And, sometimes people mix and match. Someone with an MS may go on to get a DrPH, and someone with an MPH may get an PhD.