Hello student. Both of them are different set of branches. EEE deals with elctricals and etc. Where as production engineering deals with machines and all. So, find your intrest first. Which one are you more intrested in.

Even though physics is the common subject in these both, there are different fields in both of them. In the case of answer to your question, I would suggest eee because there is a higher scope and better opportunities. Production engineering is still a developing field in our country. So there are lesser opportunities here.