Easy (funded PhD) vs Hard Path (Unfunded MS)
You said that the funded PhD offer matches your field of interest. To me this already looks like a clear win over the unfunded Masters degree. 

The only point that could direct you towards the Masters is funding. So question 1: How necessary is significant grant funding for the research in your AOI? Question 2: How much funding does the advisor at the PhD institution have? Does he already have what is needed for your PhD research or is it more like, we will apply for a grant to get money for your research? I don't know neuroengineering but for example in maths, once your salary is guaranteed, further funding is mostly irrelevant. If you find that doing a good PhD at the lower rank institution requires some success/ luck with getting funding this might tip the scales towards the higher ranked institution. But note that funding is not guaranteed there either.