Easy (funded PhD) vs Hard Path (Unfunded MS) Notes:  


I want to do PhD
I understand that ranking doesn't say much and that the professor and the research is what is 
important
AOI - Area of Interest
This question is not personal nor opinionated and can be useful to a variety of students stuck in a similar or comparable decision point.


Due to having a low UGPA (2.8), I applied to MS programs (USA) in BME (neuroengineering) in hopes of boosting myself to a PhD program that does research in my exact AOI (Unis - stanford, jhu, rice, harvard). Luckily during my application, a professor that I talked with asked me to switch to PhD since he was interested in my profile. At the end I got an offer from the university for PhD and fully funded (note that this university is ranked >150 in usnews). The only issue with this PhD opportunity is that the advisor is new (though decently connected) and does not have translational research.

Now I have also got a MS offer from a top 50 university, not funded and private (so I need a loan). Now my question is this- should I take the easy, financial free option which does research in my AOI but doesn't have much prestige and enough funding to do translational research. Or should I take the hard path and go into that competitive university (top 50), secure a high GPA and do good research to get recommendations from leaders in the field; but this option will be tough and will either be successful or will lead to failure. While the former will lead to success but will be at a much lower level when compared to the success that I get from PhD after masters.
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.