Google Page Rank is a tool of google which shows the quality of the website and web page and it fully depand upon the age of the domain, quality and visitor of the site. Alexa Ranks shows the popularity of the website which is fully depand upon the traffic on that website.
As per my concern: Google Page Rank is a type of rank between 0 to 10 which is given by Google to a site on his quality, DA, PA, visitors
There is no any limit of Alexa Rank I mean to say that if a site has 1 alexa rank then its to much beneficial for a site and if the alexa rank is like 100000 then its bad. This rank is also given by Google to a site as on traffic of site.
But my suggestion is to concentrate on promotion of site through SEO activites. If you doing SEO activities in well manner then PR and alexa rank will be good automatically. :)
We don't know when will Google PR Algorithm will update. We have to wait to see the result.PR will depends upon the backlinks.
But alexa rank will update regularly. Alexa rank will depend upon the traffic.
Alexa ranking is traffic ranking of a website as compaired to all other sites on web.It is based on the amount of traffic recorded from users that have Alexa tool bar installed over a period of theree months.This ranking set by Alexa.com.
Google page rank describes the importance of page.The basic ingredients includes richness of content,page authority,back links,keyword density,exit links,page demand.Page rank score between 0 to 10.Higher your page rank increase your chances of being found on Google.
Google Page rank and alexa rank is totally different Alexa is more concentrated on the amount of traffic you are recieving means, if you are recieving traffic on your website Alexa decreases, while Google ppage rank is the reputation of the site in the view of search engine, higher the PR higher will be the reputation and higher chances of ranking among the search engines.
Google and alexa page ranks are the ones which is used for indicating the sites quality.
In Google the page rank range varies 0 to 10
In alexa ranking the smallest value as page rank determines the quality of the website.