A lot of people put much more importance in PageRank than they should. To them Page Rank is the most important thing and they concentrate on their PageRank and often promote their site based upon its PageRank.
The most important thing should be the Search Engine Results Pages (SERPs) and where you are in the SERPs. Having a higher PageRank than someone else might make you feel good but they don't care what your PageRank is if they are higher in the Search Engine Results Pages.
Yes it happens and many of you know that. A page with a lower PageRank can be higher in the SERPs than one with a higher PageRank. It happens often.
One of the reasons I like for people to do PageRank searches is because a PageRank seach gives them the chance to see for themselves that pages with a higher Page Rank can be lower on a Search Engine Results Page (SERP) than one with a lower PageRank.
Here is a link to where you can search Google and see the results in order of Google relevance with the PageRank shown for each one so that you can see that having a higher PageRank is not a guarantee of being higher in the search results.
PageRank Search - SEO Tools - Search Engine Optimization, Google Optimization