How much do soft skills matter for admission decision?
I don't really know for PhD, but for Postdocs, from what I've seen and heard, these skills count a lot, especially when the recruitment process is well structured, as I experienced it in the UK and in Germany. Basically, the recruitment process consists of three steps: 


Sending the CV, application, reference letters, etc. At this point, soft-skill do not really count, although knowing how to write a good cover letter can help. 
Seminar/Public talk: the applicant is invited to give a presentation of his research work to a public audience (usually including the committee, and the staff from the department). 
Interview: the recruitment committee interviews the applicant. 


In the steps 2 and 3, the soft-skills are very important. Basically, all applicants reaching step 2 have good credentials, so it's somehow already established that they can write papers and solve research problems, so the quality of the talk and the attitude during the interview are crucial.