Just wonder whether the page rank will be the factor to consider when come to the popularity of the site? Any comments?
No. Page Rank is an indicator that does not have any direct effect on the SERPS. Often Page Rank and good rankings go together, but that is because the sites linking to the site with high PR are relevant for the keyword. It's always better to evaluate a site by it's backlinks and rankings than by PR alone, but as a quick judgement Page Rank is ok.
to my experience, pagerank affects how often google is going to crawl your site, how many of your pages are going to get into the index and how often they going to be temporarily thrown from the index
PR and Alexa together are a somewhat decent gauge but you can go much further. PageRank only gauges how many relevant links a page(and not the domain) has pointing to it.
why everyday there is question like this. Newcomer come and come without searching first about the past thread talking about it. here is reference