When applying for a job, what’s more important, being able to do the duties in the job description, or fill the qualifications/requirements?

When applying, it's qualifications and requirements.  If your resume/application doesn't show that you meet the qualifications/requirements that the employer deemed important enough to specify, it's unlikely you'll ever get the opportunity to try to convince that employer in an interview that you can do the duties.  

Depends on the size of the company.  The bigger the company, the more they want you to match what they have written down.

That being said, it also depends on who you are talking to.  If your initial call/interview is with an HR person, that HR person is screening candidates.  So it's important to focus on matching the qualifications in the job description.  Once you have a call/interview with the actual hiring manager, it's more important to focus on your ability to do the job.