My own 2 cents is that the application gets your foot in the door. Many programs have a minimum board score that you have to surpass before the PD will even review your application. A likable personality can be what makes you shine...
So how do they differentiate between students who all have stellar applications? When I was a senior resident, they started including me in the rank meetings, so I got to see behind the scenes. After interviews were completed, the attendings had a meeting with a Powerpoint that they'd go through and each attending had their own rank list. Each student would have a score from 1 to 5 in several different areas, like board scores, grades, publications, how they did on rotation, personality, professionalism...Then they'd "heatedly" debate during the Powerpoint section. The residents' perceptions of the students during their rotations and interviews greatly affected the rank. Like...one student really liked by the attendings on paper but disliked by the residents may go down several levels on the rank list, while others would be boosted upward.
