If you want to do "applied physics" (i.e. physics with quasi-near term industrial/commercial applications), then EE would be very beneficial so that you can get an idea of how fundamental physical theories lead to engineering technologies. Two major examples of where this overlap has beneficial were in semiconductor devices and lasers. These are two areas where the workers pool draws from both physics and electrical engineering.
On the other hand, if you want to do something like theoretical particle physics or signals processing, then it may be more beneficial to concentrate on either one over the other. Like it says in the foregoing post, it all depends.