Hello! You asked a very good question. ABET accreditation is an important sign that a program meets quality standards involving the breadth and depth of an engineering education, that the program has facilities, faculty, and support that allow them to provide strong learning experiences, and that graduates of the program have learned skills in appropriate areas and are building successful careers. Graduating from an ABET-accredited program makes it easier for graduates to eventually become licensed as a Professional Engineer, which isn’t quite as important in bioengineering as it is in other areas of engineering (like civil engineering), but I think the main value of ABET accreditation is that going through the accreditation process forces the faculty and administration to look carefully at what they do for students, and why, and how it could be better. ABET accreditation is really a sign of quality, and it’s common for bioengineering and biomedical engineering programs to be ABET-accredited, since the accreditation is such a widely recognized sign of quality.
The answer to your second question really depends on you, and what you would be happy doing for your career. Simply put, if you major in another type of engineering and take a few biology classes, you won’t get anywhere near the educational experience you will get with a degree in biomedical engineering or bioengineering. So if your heart is set on working in the medical device field or medical research, I’d encourage you to give yourself the best possible preparation for that field, and major in biomedical/bioengineering. If, on the other hand, you’re interested in medical devices but you’d also be happy working on other kinds of things as well – for example, aircraft turbines, ball bearings, air conditioners – then you might decide to major in mechanical engineering (in this example) and take some biology/biomedical engineering classes on the side. It really comes down to preparing for what you want to do.
Good luck! I’d be happy to answer other questions.