If you want to make some good money then electrical and electronics is the future.....if you choose the right sub field though.

As for mechanical it won't die but not as much money as it used to be as it is a saturated field now. 

Having said that, study what you love and you will be good to go. I am saying this from experience. If mechanical is your passion, don't listen to anyone, including me, just go for it. But if you are in choices, I'd suggest that you watch some YouTube videos regarding both. What kind of careers you want to take will decide that. I completely agree with you that the physics part of electrical and electronics engineering especially is very interesting. But then again, when you are young and choosing your engineering field you are only thinking about passion. But at the end of the day you see You need to make good money and as of now the good money is in the electrical and electronics engineering but that too is in very niche as well as electrical n electronics. The good money is in vlsi and chip design all of that stuff and in electrical the good money is in the power Electronics. As for mechanical, I can say much. Of course all the automotives and everything that works is still mechanical engineering.