Using the CoA figures from GT, you would spend about 13K for GT or 15K for Yale after your 5K scholarship. Maintaining a 3.0 is not all that easy at GT, grade deflation is definitely part of the school vibe. But GT is definitely the superior engineering school. Even so, the resources available at Yale are truly amazing and access to research is a lot easier because of the lower faculty/student ratio. Your cost at Yale is going to be far more certain since you won’t need to worry about the GPA for scholarships. Even your outside scholarship will be easier to maintain because your GPA at Yale will likely be higher.
Yale has fewer accredited programs:
http://catalog.yale.edu/ycps/subjects-of-instruction/engineering/
compared to GT:
https://www.accreditation.gatech.edu/sacs/georgia-techs-accreditation/
Note that BME and EE are not ABET accredited at Yale.
Ultimately, it is going to come down with what you want to do with your degree. If you are 100% certain that you want to be a BME or an EE and the terminus of your education is an undergraduate degree, then go to GT. If you are planning to continue on to grad school, it matters a lot less because your graduate degree supersedes your undergrad one. Yale is still mostly a LAC and you will go through the Yale core classes, which may open your mind to something beyond engineering, or some customized field of study. In addition, your GPA will probably be higher at Yale, which will help your for medical, law, and most graduate schools.
Alumni networks are very good at both schools. GT grads slot very well into corporate America, Yale grads into government, academia, Wall Street, consulting etc… Again, it depends what you want.
Next I would consider the experience - compare a private, ultra-resource rich LAC (M/F ratio=50/50) with a tech focused, urban, intense public nerd school (M/F ratio = 65/35). Things like study abroad programs are included in your tuition at Yale, and research grants are a lot easier to get if you want to study something over the summer.
So give the similar costs for you, I’d probably lean toward Yale because of factors other than engineering academics.