A good way of understanding the popularity of a website is google trend. This article on Techcrunch shows an example of obvious bad data with Hitwise (which can be applied to Alexa and Compete as well): http://www.techcrunch.com/2009/03/20/new-hitwise-stats-show-...
At the end of the day, everyone who owns a blog or a website (myself included) has been able to experience first hand how flawed the data from such companies are by simply comparing them with their own google analytics data :-)