Don raise good points... do justice to the song first...

just because there's two of you up there doesn't mean you both need to sing every song together... unless you are marketing yourself as a duo like the Everly Brothers or Simon & Garfunkel... where the singers became at least as important as the song.   It takes a really good song to break free from that kind of association.

so maybe it depends on the song and the audience equally...

I have one of John Roberts & Tony Barrands older CDs in my car and each song feels fresh... maybe because they don't get themselves locked into a certain "sound", but pick what seems to work best for the song.