Choruses and even songs where people are liable to join in all the way through are ok in their place, and can give a great sound sometimes with people sticking in their favourite notes and counter melodies.

But if I'm in a room, singing round it, I'd much sooner that much of the times it's people singing songs without choruses, or songs I haven't heard before, or recently, or in that particular variant, which isn't the same as the one someone famous recorded.   

Maybe there's a distinction to be made, on the one hand, between "song circles", mostly choruses and singalong songs, which are primarily about joining in songs, and on the other hand "singing circles", which are more about sharing songs.