A ecllage degree in EE is one thing, and work in Electrical Engineering (not an office/paper/sofware pusher work) is totally different potencial all together. Working on with low power systems is one and working with high power systems, where probably most of the still original/fundamental work currently exists, is a tottaly dfferent thing. Working for joy (sort of hobby) is one thing and working for pay is another, in the EE unlimited field, of course if one is lucky to have both of them in one that is the best, but in reallity these are very selective jobs.
Knowing how to solve differencial equestion, does not make one a good engineer, especaially an electrical one (as going through a medical school, and having high grades, does not make one a good medical doctor) these are the basic building blocks that are good to know (altough who knows, and with a sufficient intelligence and good funamentals one can easily pick them online, these days), but as with every knowledge knowing it (whatever that means in ones mind) does not translate to a good practical usage and even lesser to a original one.
In addition, the "knowledge" pushed in the EE education, is highly tailored for maintance/support and development work a narrow direction of a vast field. The most intersting and practilcally useful work one does not learn at school but in the field, by making, blowing up and testing stuff.
So, EE should be chosen because one enjoys it and not because, one needs to have a job. Technically with a good analythical skills one can get into many jobs, that requires high level of analticial thinking, but not much predefined field knowledge, after he has been in the EE field.
As disclosure, I am coming from the high power EE field, although in my high school years, back in Estern Europe was designing and builidng transistor schemas, but for the past 13 or so years, I working on massively scalable software (HPC) systems, but continue doing my highly enjoyable experimental work, in the field of high power (di)electro/magneto-dynamics as a hobby. This work, although not paid ( in the standard sense), brings a lot of joy and substential amount of real savings (some times of several thousands, as off-the-grid systems design and setup) , in anything that has to do with electrical systems to me and a good number of my friends.