Interesting question to which I don't have a fully coherent answer.

Under the broad category of musicians are people who do very different things. In our group we have a guitar player whose focus is on playing the guitar and a harmonica player whose focus is on playing harmonica. I sing and play instruments but my focus is on writing the material we do. We have another guy whose orientation is as an entertainer.

When I'm writing songs, I'm a musician. When I'm assembling a set, I'm aware that I'm responsible for 45 minutes or whatever of the audience's lives and I want to make it the richest 45 minutes I can. That doesn't always consist of entertainment in a narrow sense--it may include challenges and surprises--but there had better be some entertainment or there won't be an audience. Maybe I'm lucky, but I can basically do what I want to do as a musician and have an audience find it entertaining.

A long way of saying I agree with those who don't find this an either-or kind of choice. Or, yeah, both.