I am a student in Engineering Physics in the U of I.
Basically you can get a degree in physics in one of the four ways: Engineering Physics (degree awarded by the College of Engineering), LAS Physics (Sciences and Letters), LAS Specialized Curriculum in Physics, and LAS Physics Teaching concentration (degrees awarded by the College of Liberal Arts and Sciences). The Department of Physics, however, is in the College of Engineering.
There are a number of options in Engineering Physics, like professional option, biophysics, computational physics, optics, electronics, etc. The professional option of the Engineering Physics is almost the same as the Specialized Curriculum in Physics in LAS. The only differences are the foreign language requirement and the general education requirement between the two programs. College of Engineering has easier foreign language requirement, but LAS specialized curriculum has less gen-ed requirement. But after all, students in both programs take the same courses offered the same department. They are considered as the more "hard core" programs in physics.
On the other hand, the LAS sciences and letters curriculum is considered as an easier way to get a degree in physics (because it requires less core courses), but it is very flexible about multiple majors and minors (multiple major is not allowed in Engineering physics nor LAS specialized curriculum). However, in the sciences and letter curriculum you will have to fulfill a whole bunch of gen-ed courses (Note that LAS sciences and Letters has different gen-ed requirement with LAS specialized curriculum).
If you are in the CoE already, I would suggest you to switch to engineering physics because it's much easier (ICT is really annoying). However, if you want to do a double major, then go for LAS sciences and letters.