It depends what kind of personality you have...so the answer to your question is unreachable or both. Neither one is better...they just are. One would be terrible for a very focused person, the other would be terrible for a more complex person.
Know thyself...then you can be well-rounded or master.
It depends on the persons themselves. I am included a well-rounded one. The advantages of being the one like me is I can handle many problems by myself, especially the common problems (no so complicated). I can play some musical instrument (guitar and electone), I can sing, I can do gardening, I can do plumbing, I can do something what electrician and mechanics do, I can weld, and I know enough the things around other professions. All of the things really support me as an English teacher. But, actually being a master at a specific skill also have many advantages, and the very especially one is he can be the expert on that part, and he have more time to socialize with others because he is demanded to ask for help to other people at the time he is faced to something out of his specialization.