I got my undergrad degree in physics and switched to EE for my master's. I've since switched
to neurophysics. I was somewhat disappointed with the whole philosophy behind engineering after having been trained from a scientific philosophy. Anyhow, I still like physics, I still work in physics while I pursue other education goals.
EE has probably has more job availability than physics when it comes to working in your field, but a physics degree is pretty versatile for if you want to work outside your field. For instance, think of how many managerial positions in any number of industries you could get into simply by putting physics degree on your resume. You can go into medicine, engineering, or even business after a physics degree if you wish to continue your education. Or you can teach, of course.