Google looks for pages that are trustworthy and relevant. If two pages score equally well from a MatchScore perspective, google willy try to pick the page that have a higher PageRank. There are other factors that come into play too, but PageRank and word relevance (MatchScore) are the two factors to look out for.

Pages that are dedicated to a subject - and surrounded by pages on the same subject - can appear earlier in search results (because that gives them a higher MatchScore) than a single piece on a high PageRank page like the NY Times.