To be given a high pagerank in alexa i think is a great feat, since they monitor all website globally, and country per country. High chance alexa has a more accurate count when it come to rating a website. one of their main function is to rate a website pageranking.
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Page rank matters this has been devised by google to tell surfers , ad agencies and others that the website is an authority site and is refered by others . Page rank can be achieved through various methods including article marketing , commenting on to others sites , video marketing , social networks etc the point is to get people talk about your site link your sites for information , comment on your site . Thus Higher the page rank more is the popularity of site on net . Advertisers also prefer website with higher ranks for their ads hence to make some money out of your web site you need work improving on page rank . Page ranks is arrived with complex alogrithm devised by google which takes so many factors important are whats the age , how many sites links to the site and updates . you can refer SEO experts Brad Callen work on this

Alexa rankings should be considered as most important factor for a site as the rankings improve you can then monetize your site and earn handsome income from your site .

Twitter following is another important factor in Internet marketing . It gives you instant feed back on your product ,article s .People love to comment on things which matter most to them .
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Traditionally page rank has been very important. It determines position in the Google search engine. Much traffic still comes from Google, however, new mediums like Twitter followers are changing that. Google is actually on a path to quash page rank, and instead be able to parse pages for the best information. Page rank can and has been gamed, and new methods for ranking websites are on the horizon.

My advice is to build high-quality pages/sites, promote them through new mechanisms like Twiiter and Digg, and don't focus your efforts too heavily on page rank.
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O my I just wrote a big explanation and then closed the window by accident ... grr. lol

Ok very quickly compete, quantcast and alexa measure traffic they have nothing to do with page rank...

Page rank puts you in a class of popularity, who is linking to you and how popular are they and how popular are you. This would take meaning when ranking for certain keywords on your site.

Example. I have a pr of 4 you have a 3, I would beat u out if we had the same optimization.

Ways you could beat me out with a 3 if i had a 4:
Better h1 tags, Better Meta title tags, More content. These are probably the most biggest factors when ranking in any search engine. Google is the only biggest search engine that uses pr, however they are the biggest so it is important. Yahoo is the second biggest so dont count them out, I get just as much traffic from yahoo as I do google because yahoo updates more often and also consider that google is a informational search as to yahoo is more used when shopping online... Because google I would say is more for internet geeks as where yahoo is used by someone that might not use the internet as much.. this is my personal opinion, im not sure if that is true so dont quote me on that.

Well I hope I have answered some of your questions here.. If you need more help please feel free to ask, I would be glad to help.

Thanks Mike !
Source(s):
google.com, yahoo.com

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There's all types of varying opinions on the subject and you'll find that PageRank, Alexa, Quantcast, Compete, etc all have different system for rating content so you can't necessarily take one rank and compare across all system since they use different data and analysis to base their final rating.

From what I understand, PageRank affects both Crawl Order and Crawl Depth. Crawl Order means the order in which google crawls the web and the higher the rank, the higher your are in the order (which is good) and Crawl Depth apparently means that google will allocate more 'crawl budget' towards your site if you're ranked higher. Other than this, PageRank isn't a direct reflection of you site's actual ranking and is more a popular contest of who is linking to your site. At this point, I think there's a general consensus that putting emphasis on PageRank is pretty unnecessary as there's really minimal actual impact that it has. PageRank is more related to SEO (search engine optimization) than page ranking.

Alexa, Quantcast, and Compete are really different beats in comparison to PageRank as they rely more on traffic volume to acquire their rankings.

As for what matters, that really depends on what you're looking for. Do you want to know your potential growth on the web, your users demographics, how fast you could potentially spread information or something else?

For example, since twitter is so viral, it could potentially be more useful to have 50,000 twitter followers than 150,000 members from an online community. However, if you're a company and want to focus in on your user-base, you might value Quantcast more since it breaks it's analysis into demographics, age, region, etc. So to answer this really requires limitations on what one is looking for.

Generally, I think it's more important to use such information to see the rate or value of change rather than seeing a direct influence. If you're steadily moving up on PageRank, getting a lower Alexa, Quantcast, and Compete ranking, then it's clear that something is succeeding. So for a business, this would be valuable internal information.

It's definitely an interesting topic and has been debated for some time. With the increasing amount of 'types' of websites, I think that each one of these services can appeal to different crowds and there's isn't necessarily one service that provides what all of them do.
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Alexa probably is the most relevant because it tells you how many people your website reaches. But the honest truth is none of the above are as important as your web site's position in the search engine results page for your keywords
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