Ooh, tough choice. Personally, I would choose Howard. (For reference, I went to an HBCU too - Spelman. I have friends and colleagues who went to both Howard and FAMU, and considered both myself for college.)
The factors are up to you, really. Florida A&M has great engineering programs, especially given the shared engineering school with FSU. I have lots of friends who went to FAMU (it was pretty popular from my all-black high school - many of our teachers were alumni of FAMU) and majored in engineering and went to great graduate schools and obs afterwards. The social life in Tallahassee is crazy! In a good way, I mean. Tallahassee is a decent small city and a good place to be a college student. All my FAMU friends had an excellent time in undergrad.
However, FAMU’s biomedical engineering major is really a concentration in its chemical engineering major, and you could probably recreate or approach it by major in chemical engineering at Howard if you wanted and adding some classes in biology. And Howard’s school of business has majors in supply chain management and information systems and analysis; you could probably major in mechanical engineering and minor in one of those to approximate the industrial engineering major. Other than that, the two universities’ engineering offerings are really not that different.
But…Howard is the Mecca! Howard’s social life is also crazy good, with people traveling from all over to go to Howard’s homecoming (although to be fair - they do the same at FAMU). I do think DC is a better city to be in overall - more opportunities for internships as well as more things to do if you just want to get away from the campus scene for a while. Howard is also by far the better reputed of the two - it’s one of the top HBCUs, has great on-campus recruiting especially from companies that are trying to increase their diversity, and consistently does well in the big prestigious national fellowship competitions.
One smaller thing to consider is that if you intend to go Greek, the Greek life at both universities is intense but Howard’s, being the home of 5 Alpha chapters of NPHC organizations (plus the Beta chapter of another and a single-letter chapter of a 7th), is probably the most intense.
However, I am pretty sure that both of them do Fried Chicken Wednesday 
(Why does every HBCU do Fried Chicken Wednesday? Spelman and Morehouse did it, too.)