To answer some questions about JHU:
The difference in annual R&D spending between the two schools is significant (Hopkins outspends Duke 2:1 annually, and when just looking at Engineering R&D is outspending Duke about 14:1) and I believe this is a reasonable way to assess where more opportunities for research experience are available and the likelihood of you finding research in a field of interest. ( Source: http://www.bestcolleges.com/features/colleges-with-highest-research-and-development-expenditures/) Additionally, Hopkins has built its name around its healthcare empire, so, when coupled with its unparalleled research spending, it is unsurprising that the undergrad and graduate BME programs are some of the institution’s premiere programs.
That being said, this by no means suggests you can’t find what you’re looking for at Duke, but I think it is wrong to suggest that these two schools are on equal footing when it comes to research opportunities. Baltimore is also next door to Bethesda, which is the NIH headquarters, and there is significant collaboration between Hopkins and the NIH (and many NIH labs are located in Baltimore). Nonetheless, the onus will ultimately fall on you to reach out to professors and labs to find suitable research projects. Additionally, if the undergrad JHU BME program has any bearing on the grad program you speak of, then it really will be a hands on experience with an emphasis on design: http://talk.collegeconfidential.com/johns-hopkins-university/1881734-choosing-between-bme-at-jhu-and-bu.html#latest
I’m not familiar with the Master’s program, but having completed my undergraduate there I can answer general questions about JHU, especially the infamous rumors of Hopkins students having no social life and Baltimore being a war zone (both of which are not true). Lastly, the grad program will be on the Homewood Campus with the undergrads (and this is a very different environment than the medical campus - more suburban, quieter and scenic), so much of this will apply to you:
Social Life and other common non-academic questions: http://talk.collegeconfidential.com/johns-hopkins-university/1878658-johns-hopkins-vs-cornell.html#latest
Lastly, I did have friends complete the Neuroscience Master’s program at Hopkins, and it was a similar setup with one year dedicated to coursework and a second year primarily for research. The idea is that you completely immerse yourself in your research spending 8-14 hours a day in the lab much like an actual researcher. I think this truly gives you a research experience and prepares you for a career in research (and you tend to get better research outcomes when you’re truly dedicated to the research without the distractions of other coursework).