Alexa is a tool for checking your website rankings, which will have development strategies more appropriate. Alexa ranking is only relative in nature. Alexa is based on the algorithm of the amazon. PR is based on statistical algorithms of Google. So I think that PR is more important than Alexa. You see some methods to increase alexa rank. http://forum.sangtao24.com/seo-sem-talk/methods-increase-alexa-rank-t493.html
Alexa rank only provide the information that how many visitor visit to the website, & most important page rank of the website which shows the quality of the content into the website.
According to me PR is important. Pagerank can be very important for any sites that depend on traffic from Search Engine. Might be possibility that you will be ranked higher than another websites if you have a good pagerank.
Pr is more important then alexa rank. Pr show your site importance in google views, where alexa shows your site traffic.
Page rank id too important in creation of rank high on the free (organic) search results for Google. which working too fast as compare to Alexa.