Why does your dad want you to go into investment banking? The raison d'etre is money, and with that comes intense pressure to perform and make profit for the shareholders and stakeholders. You also have to think of the working environment and the type of people you will end up working with.
Engineering is real in that you have something solid to show for your efforts. I don't need to tell you, the sky is definitely not the limit and you have the choice of working on some absolutely amazing projects and be proud of your achievements. Just look around you, virtually everything you see from the smallest to the largest that is man-made is the product of an engineer.
And then there is physics. As Chlorophile points out, if your motivation is to push the boundaries of human knowledge, then money becomes secondary and you will find that everything else will become relatively insignificant. There is a synergy between physics and engineering where the hypothesis needs to be tested. The really interesting stuff is pushing the existing technologies to new limits.
It may well be that working as an engineering physicist will kill two birds with one stone for you. Think big like ITER and it's successor, international projects etc.
I know of quite a few physicists who went onto engineering as a career, but relatively few engineers who went on to become physicists. That is not to say it does not happen, just less likely.
But be certain, that whatever career you go into, it is because YOU want to satisfy your passion and NOT because someone else thinks you can make loads of money. The latter is likely to leave you unsatisfied and somewhere down the line, deeply regretting your choice.