Google PR is the most important those who are depending upon google search engine. If your google PR is more your website keywords will be given more priority in Google search Engine. There several factors are in consideration for listing website for a search keyword. However pagerank plays an important role for google search results.
But Alexa is not a search engine. Which monitors the http request and given rank according to the successful http connection. All the http request monitored through the alexa toolbar, if installed.
I look at it from the other angle.
If you want to monetize your blog through sponsored reviews or selling text links, then Blog PR is extremely important. Blog PR is one of the most important factors affecting your income.
If you want to get juicy backlinks, then Google PR is also very important. If you can get a couple of backlinks from PR7 site, that will matters a lot.
I will go with Google PR than Alexa. Even you have good alexa rankings, it’s not sellable. That’s why business blog with high PR is great because you can sell it in good price.
You sound like the sort of person who prefers helicopters on their sandwiches rather than submarines on their sandwiches due to sandwiches that aren’t soggy being more sellable.
I don’t know why your bothering Stephen 
When it comes to SEO no-one’s going to listen to the one person making the claim that PageRank has little to no value because they’ve been conditioned over years though bad articles, misinformation and wonky advice shouting at them that the opposite is true. 
Absolutely, and then of course there’s 1,001 ways to skin a cat (so to speak!). SEO is not a case of using only one method OR the other, you just need to leave no stone unturned IMHO
If you are selling adspace on your site then PR is crucial. If you are going for keyword positioning just spend the majority of your SEO time backlinking for those terms.
Obviously Google PR .Alexa ranking is very unreliable.
Which is better something that is totally meaningless (such as Google PR) or something that is totally meaningless (Alexa)? I vote for the totally meaningless one as it is more meaningless than the totally meaningless one.
PR is important but rather than that the site must have a lot of visitors daily and make some SEO technique that can boost your visitors.Let Google decide on what your PR will be 
Only to those who are obsessed with some form of visual feedback that doesn’t actually mean anything.
I honestly think Alexa ranking have zero creditability there’s tons of articles telling you how to fudged your rankings… As far as I know Google PR can not be easily manipulated…
heres a quick result on google for “fake alexa rankings”
http://www.google.com/search?q=alexa+fake+rankings&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
yes it can - you just create a million junk links from other sites to your page and you’ll instantly have a high PR.
neither Google PR nor Alexa but Google Search Engine ranking is more important that gives you traffic as well as business so i think that is more imporatant than Alexa rank or google PR.
thanks all, your answer very useful :):)
Nonsense
Perhaps Yahoo doesn’t post junk stats intended to distract the morons from disrupting their main business. Perhaps they don’t have so many people trying to rig their results the way that Google does and so don’t need an equivalent to Page Rank for the idiots to waste their time trying to get good results from even though those results mean nothing whatever when it comes to how they determine the order of pages in the search results (except as a last resort when they can’t find anything else to select between them on).
i always focus on good serp i never focus on google pr or alexa
Alexa is just a very ‘basic’ indication on how your site is doing and i would treat it more as a fun indicator so basically i dont take much notice of it really,regarding PR once again this does not carry the Kudos it did a few years back and in my eyes is only really any good if you are either selling your site as that makes a great selling bonus and i guess hence you can command more money if it has a higher PR and the second good thing about have a PR or a high PR is when you selling advertising slots on your site as with a higher PR you can command more money.But if you dont plan on selling your site or selling advert slots PR does not mean a great amount.
What in my eyes is king but has not been mentioned is traffic and quality traffic,i would have this latter option any day.
Google Pr