I teach Physics and have a research lab at a modest sized state school. Here's my $0.02 - you should do what interests you. I know that sounds pollyanna, but with the economy in the state it is in, it isn't clear that an EE degree will be more marketable than a Physics degree. I know quite a few out of work engineers right now.
No degree is a sure thing for getting a job right now. The experience that goes along with the degree is what makes you marketable. You should plan on doing a co-op, internship, or research project (maybe more than 1). You should aim to develop a set of skills. For example, students that work in my lab work with optics, electronics, vacuum equipment, lasers, and other stuff. They learn surface characterization techniques like scanning electron and atomic force microscopy. I really try to help every student to be a coauthor on a journal publication. They do poster presentations, etc.
Admittedly, most of the students who work in my lab are intending to go on to graduate school (or med school), but those that do look for employment get it and they usually impress the interviewer. The interviewers rarely care very much about GPA or whether the students have an engineering or physics degree. They're happy to know that the applicants won't sit on their hands and can roll up their sleeves to get stuff done.