I haven't finished my undergraduate either but from what I know
physics major is more fundamental
where as EE just take the work of other people, (what has already been found).
common joke my friends who wanted to be EE said "physics do the proof and make formula. We use them"
If you want to be inventive, they're both way to go. Sure you'll have to do more proofs as physics major then EE, but if you want to invent stuff, imo they're worth it.
I guess i'm just stating the obvious xP
anyways, if you major physics major, you don't have to be stuck up with proofs all the time, you can invent stuff after your degree (or before).
Proof is for more for those who want to be pure physicist(and i'm not just talking about degree here).