I work as a physicist. I go into work everyday. I get on the computer and read my Email and answer it if necessary. I confer with other physicists and engineers regarding the strategy for an upcoming paper or novel computer model. Sometimes there's mundane work like making sure the figures in a paper are 600 dots per inch, the colors are right or some such. Many of my colleagues are encouraged to write grants, but I am not currently in that line of work because I am bringing many computer models, and software that has not been used in years up to speed.
It would be easy to dismiss my job as a computer analyst, but it is far more than that. Results have to be analyzed using a physics perspective, as often programmers and managers may not realize shortcomings in the model and improvements, not only in algorithms, but in the strategy for using those models in the most effective manner.
My managers who have earlier been involved in the same work recognize the contributions of my colleagues and myself. As a physicist, you will be highly regarded. Some of my colleagues are involved in experiment and I have not been involved in experiment since early days on a training assignment.
I often work along side with electrical engineers and I have a background in control theory, and spectral estimation. EE's can often do the same things as physicists in the day to day activities. I see some of my friends who are EE's working along side physicists in plasma physics research. All told, it impossible to say your day to day activities as an EE will be any different than if you remain in physics if you do plasma physics, computer modeling, or applied physics. In academia, EE's will often encounter the same pressure to publish and bring in money as physicists.
The supercool discoveries are rare, if they were common they would not be supercool. Advances in physics are not necessarily paradigm shifts and advances in EE can be as powerful.
This may sound trite but I always considered physics to be a journey, not a destination. I did coursework in physics because I liked it, not because it could do something for me later. I did coursework later in EE for the same reason, although I did not get degrees in EE. Currently EE graduates have better job prospects and pay than physicists. The day to day work may not be much different.