I am not entirely sure if it is better to be “a jack of all trades” than a master of one trade. I feel that they both have their advantages and disadvantages.
I will start off with the advantage of being a master of one trade. Some companies would rather hire a chemist to work in their chemical lab (since they are experts at chemistry) if their primary goal is on focused on chemical innovations. They would not want an employee who knows “a bit” about chemistry to handle the lab.
However, with companies that are not so specialized in a certain field, like medical device companies, this is where knowing a little of everything is useful. Since medical devices require knowledge from different fields, hiring a Biomedical engineer would be more favorable as opposed to an electrical engineer who only specializes with the electrical aspect. I believe that becoming a BME can have its disadvantages, career wise, yet it is all depends on what type of company you are applying too and what they are expecting.