I don't think the two are mutually exclusive. You need both variety and focus to excel. The key is to know when to shift gear between the two modes. Why don't you just do whatever that you find fun and challenging? That's usually the best indicator of what you should do.
Yes. Donald Knuth sometimes quotes Huxley - a good education is learning something about everything and everything about something. There should be a center to studies or you're all over the place, but having extreme tunnel vision is not helpful either.
