There are a few different paths when it comes to aerospace engineering with respect to "avionics".
If you want to be a guy who designs the boxes, you should pursue a degree in Electronic Engineering.
If you want to be a guy who designs the systems on the airframe “using” the boxes you should pursue a degree in Aeronautical Engineering in one of the electronic/avionics streams.
My personal opinion though, is that good avionics systems engineers are few and far between. You need many years of experience to supplement the typically weak exposure to real world avionics that most programs offer. (IMHO)