which one is more physics based? which one is more prestigious?
As I tell my children, google search for the top 10 paying degrees.
Two of my classmates in EE were physics majors, they found it was tough to get a job without getting a Phd so they took the EE route.
Most prestigious... thats kind of a loaded question in a forum, but your professors can offer advice here.
My advice? Go for EE, take a lot of CS classes (make sure you take C/C++ over java. Focus on systems design / compilers) and take a few digital classes.. I worked pretty close to the metal for most of my career, but I had a career that spanned all levels of engineering and across disciplines. Then start buying real estate before you are 40 and become obsolete in the field and become a landlord... which makes it a lot easier to retire before you are 50.
I tell my older daughter to check out the actuary field, man what a gravy job and it pays well for smart people with backgrounds in math and physics.
This really depends on the program/adviser if you're talking about research. Also it depends on the culture which is regarded as more prestigious, but I think chasing prestige is rarely a good idea anyway. An Iranian friend told me that electrical engineering is considered the highest field in Iran, whereas a friend from China told me that mathematics is considered to be the highest field in China, so the silly field hierarchy will vary from place to place.
Separate names with a comma.