In my mind - they are one of the same thing. So it's not so much 'versus' but how they compliment each other. One health is a more recent concept and, I believe, it's there to try and reignite the fact that global health initiatives have stalled a bit over the past decade or so. It works for many disciplines that, if the original targets are not met over a period of time, then 'rebrand' the product to make it seem like something new - and to try to recruit a new audience. That's my spin on it.
My understanding is that one health is a strategy to specifically address zoonosis - it is the name of a specific strategy which various bodies are involved in, including the European Union: http://eeas.europa.eu/health/pandemic_readiness/index_en.htm . Global health is a much broader concept, which is also normative. I've written a discussion paper with a colleague on definitions of global health, and the evolution of global health, which I attach here.
Working Paper Discussing a definition of global health: Global health dipl...
They are both comparable, but what sets Onehealth apart is the specific mandate of the Onehealth approach to bring together animal health and human health. The increasing threat of emerging and re-emerging infectious diseases and the poor integration of animal health within global health initiatives could be seen as the inspiration behind OneHealth.
I see One Health as broader than Global Health. Global Health is worldwide human health; whereas One Healh additionally encompasses veterinary medicine and environment health. Zoonosis is one major focus of One Health (interacting with both the human animal relationship but also with the environment - climate change plays a role here too because of shifting and water and arthropod vector distribution patterns), but not all there is to it. Other areas include but are not limited to food and water security and impact of natural disasters on both human and animal health (and climate impacts here again of course).
t an answer, more a question: anything new about this ? My feeling is you adress a proper question! In a animal health perspective, my understanding is that actually "Global Health" is a view from the human medicine side, with few (if any) interest for animal health, including a very limited interest for ecology of zoonotic diseases. Then I wonder if you still are interested by the issue ?
I think "global health" refers to the study of disease epidemiology worldwide (not from a local perspective), while "one health" is more about the link among animal, human and environment in determining disease/health, both in local and in wide perpective.