Electrical Engineering (EE) and Computer Engineering (CpE) programs have similar curricula, but different demographics and student outcomes. This paper extends earlier longitudinal studies to a larger and more diverse dataset with 90,000 first-time-in-college and 26,000 transfer students who majored in engineering at USA institutions, including students who started in first-year engineering programs, those switching majors, and those transferring from other institutions. Black men and women and Asian men in engineering are strongly attracted to EE when they start in college. Black students and Asian and Hispanic men are attracted to CpE more than other engineering disciplines, but at lower rates than EE. Asian students have the highest graduation rates in EE. EE students are much more likely to graduate than CpE students. Compared to other engineering disciplines, CpE graduation rates are low for women of all races/ethnicities and Black men. Both EE and CpE lose many of those starting the programs, but switchers and transfers compensate for some of the loss. Considering Asian students and White men, switching to EE accounts for the high attrition rate from CpE, but attrition in other populations cannot be explained so easily. Trajectories of student enrollment differ by race/ethnicity. The approach used here could serve as a model for other fields studying their own demographic distributions.