What PageRanks do your competitors homepage have? If your site is a PageRank 1 and your competitors' are a PageRank 9, there's no way in hell you're going to be ranking above them in the foreseeable future. However, if you're a PageRank 4 and they're a PageRank 6, with a little dedication, you'll be able to chip away at that gap and eventually pass them with a long-term plan.
Alexa ranks are a completely different beast. A site may rank 100,000, and yours may rank 800,000, but your site may very well receive more traffic that the other does. This is because Alexa gathers data from users who have decided to install the Alexa toolbar on their browser. So, if a site has a group of Alexa users that happen to frequent their site, their site will be artificially inflated. If the Alexa rank is in the top 100,000 there is a fair amount of data gathered and you can be more confident in Alexa's results.
