Checks decide the winner if NO ONE has any keys of the Final 3 or if EVERYONE has at least 1 key.
Health and comps are also important. The final comp could also determine who wins. But, the main thing that decides the winner is checks. The person who had the most checks will win.
(So, if you have NO keys. And someone else has at least one key. You will not win come Final DC no matter if you have more Health/checks or how well you do with the comps)