Both have music in common.
It's the versatile human voice singing meaningful words versus vibrant, colourful body language which can be very moving as well as visually beautiful. For me teaming up singer with dancers does not always work, say when the two sides disagree on interpretation or have very different personalities.
Unlike solo song or solo dance, a ballroom and latin duet have the additional appeal of partnership, the magic of man and woman.
But song does have a trump card. Like radio and unlike TV/PC, a song needs only an ear when the eyes are busy elsewhere.