According to me authority of a Web site is important because it is often used to determine the weight given to links to your Web site. A link from a large Web site is better than a link from a small new one, and a link from the main page of a Web site may help you more than a link from a back page of that Web site.

Yes quality link is always important, referring to your line I would say one quality link is far better than 20 low quality link.