I say it would be a tie.
Cancers have an emotional strong willpower but Capricorns have a practical strong willpower. They're both opposite signs of the zodiac as well-- meaning one has what the other lacks or needs. So I can imagine Capricorn backing down for the sake of practical reasons and letting Cancer win or Cancer backing down for the fear of creating more damage than what was already done emotionally and letting Capricorn win. Cancer has a heart and Capricorn has a brain.
