Anthropology vs. Religious Studies graduate programs
Think of anthropology as more scientific and religious studies as more historical. Or Hard science v humanities, if you find that distinction meaningful. The processes of each are a bit different. 

I'll just guess that there are more opportunities in anthropology and if you are on the cusp of the two fields there are probably more things open to you with a credential in anthropology than if it were more religious studies based. 

Being associated with a broader field is an advantage in that it gives you flexibility to choose, even if you choose a narrow part of it. Being associated with a narrow field is probably a disadvantage. 

Graduating from a "top" institution is a benefit for your first job, most likely. Graduating with great recommendations from recognized experts in whatever field is a bigger initial advantage. 

I suspect that you know that some "religious" studies folk are more interested in preconceived notions of how things work and more interested in proselytizing than in learning. Avoid those sorts of things and you should be fine. 

Obviously this is not a real answer. That can only come from you. But discussions with people you know is a good way to explore it.