Obviously the two are not mutually exclusive but perhaps it's about where your priorities and duty lie. Is your first duty to do justice to the song or to entertain the audience? (I'm a singer rather than musician but I expect my argument works with tunes as well.)

I remember once (in a pub, not at a paid gig or even at a folk club singers' night) stopping a song (Francis Tolliver) after one verse. It wasn't because I wasn't entertaining the audience, it was because I shouldn't have started that song there – it wasn't fair to the song, its composer or the people who the song was about.

I'm only an average "floor singer" and certainly no entertainer but I do feel I have a duty to my songs to sing them as well as I can, to keep them alive and pass them on so that, hopefully, someone with real talent will take them away and do the same. That won't happen if the songs and my singing aren't good enough to merit some attention, so I try to choose songs that match the venue/audience – but I do it for the songs and not the audience.