Have you considered ROTC? You will finish a 4-year degree in your chosen field followed by 5 years of active duty. The nuclear field is an option, and you will serve as a division officer and gain management experience. Upon resigning your commission, you will be eligible to work for companies like GE, which recruits junior officers.
There are a number of slots available for enlisted to go ROTC, but your best chances are to join ROTC while not being enlisted. They already have you in the Navy if you're enlisted, and you will need top recommendations to get ROTC. As a civilian, ROTC is a great recruiting tool.
For your original question, CE vs ET.... A typical job for a CE at the individual contributor level is circuit board design. You'll learn about different microcontrollers, FPGAs, chips, VHDL. A typical job for an ET is troubleshooting/repair. You'll learn how to maintain, tune, and fix systems. Both jobs can be hands on and both jobs can be at a desk/bench. Both can be high or low in pay. In the Navy, I doubt you will do much of either design or repair. A Naval career will be focused on steaming a ship through water to project power and put ordinance on target. Your primary purpose will be operations and preventative maintenance. And keeping the bilge clean!
For the Navy, officers are the managers-in-training, managers and executives. The enlisted are the workers, supervisors, and managers. What are your interests? Where do you see yourself in 5 years? Have a goal and work toward it.
Dave