I think electrical engineering is a great field, whether you like it or not. I have great respect for engineers. In fact, I'm watching a series now trying to learn physics from an engineering perspective rather than from a traditional theoretical physics perspective. When the knowledge is "applied" and practical, you gain a different understanding of it. I wouldn't go as far as saying "deeper," but having multiple perspectives helps me especially, tremendously.
Just as an example, I got much more out of this one lecture on lagrangians than I did in the whole classical physics course given by Susskind:
I took a class at my undergraduate college called "physiological psychology." It was given by the psychology department. This was a small college in the wine country of northern California and, believe it or not, this class was the closest thing to neuroscience that you were going to find there. And I was a biology major.
In any case, the professor was great and actually became a personal friend of mine over the years. But he used to like to "preach" to the class at times. And these were great moments. Real human learning. One of the things I remember was that he actually went to medical school to become a psychiatrist. What he learned almost instantly, though, is that medical "doctors" on the inside are basically divided up into two categories--surgeons and non-surgeons. If you're a surgeon then you are cool and you have street cred. If you're an internist or a family practitioner, you're basically a nobody. So he quit medical school and became a clinical psychologist. But that didn't work out either. He gave this mimeographed handout at the end of each semester called "Looking forward backwards," which was basically an alert to really think about what you want to be doing day to day in your chosen profession. And to really think about it. For him, he thought he would enjoy being Freud with patients sitting on the couch. But what he found out, the hard way, was that he was spending 8 hours a day, day after day, listening to people whine about their problems that he didn't really care about. So after yet another painful and expensive career change, he finally found what he loved, being a psychology professor.
But my point is that I drew a correlation between the "surgeon" and the "engineer." I think the engineer is to the physics world what the surgeon is to the medical world. The engineer is the one that gets things done and applies the science. The theoretical physicist has his head in the clouds. So I have great respect for engineers even though I'm more of the theoretical type myself. Bottom line, though, is that, unless you are really unhappy being an EE, this is not a bad career choice. Btw, speaking of engineers, this series really cemented by admiration for engineers: