I do tend to do both. However, we're a three-piece and I sing BVs, so I have little choice but to engage with the audience to some extent, and that's good, because of all what Oldgit said.
My natural style, however, is neck gazing. To some extent, that's because I'm so happy to be able to do this, and I LIKE seeing myself doing it, as it were...
Cripes, I'm even doing it over there <<<