I am wondering if it is better to take a year off during medical school to do a fellowship at the NIH or to pursue the Fulbright route.
Got it. The NIH program, CRTP, can only be entered after you complete a year of clinical medicine (i.e. for most schools, you can only do the CRTP between your 3rd and 4th year). Technically, you could do a Fulbright between any years, but usually you would do it between 2 and 3, or 3 and 4. With the Fulbright, you could apply to do basic/clinical/translation/public health research (some countries though will not accept applications for projects that are too medicine-y).
Is one more prestigious than the other? Eh. The point of taking a year off is to learn more about the field you are interested in, try and get research published, and to network like crazy. Programs like HHMI, NIH, and some of the Doris Duke sites are great because they guide participants into productive labs that will lead to publications. With a Fulbright, it's difficult to tell if your project will be successful. Besides, it's difficult to network with American program directors when you're living in Finland.
A few years ago, I was a finalist for a Fulbright my senior year of college, and since then, I've thought about reapplying. However, due to the points I enumerated above, for a medical student, I just don't think a Fulbright is as good of an option as an HHMI, DD, NIH, or Sarnoff Fellowship. Then again, if you are interested in public health or a field that cannot be studied in the US, a Fulbright is a great option