I don't know any business that pays attention to Alexa numbers. After 15 years of building a lot of Web sites, no one has ever brought it up except on forums like this one. GA directly measures a site's actual traffic. Alexa takes wild shots in the dark. It's as unreliable as Compete or Quantcast.
I'm going with Google on this one. More in-depth over Alexa. I do find that these third-party sites to have thrown off my stats a lot but I don't mind them considering that they are utmost general guestimations. For those saying that Google is "bias", I can't really see this being that it is in fact the most used search engine on the web...
Google Analytics is the best of the best any doubts now ? The reason advertisers use Alexa is pretty simple. It is the public accessible data, so anyone can read it. In the case of analytics you have to contact the webmaster of the site and ask about the data, which would be hard or impossible to get. Alexa may be not accurate, but you can read plenty of info out of it.
First, regarding Alexa, it's clear that the system has its limits: Alexa largely depends on the number of people using its toolbar. There can be some controversy over how representative Alexa's user base is of typical Internet behavior, notably for low-traffic sites. The largest is the community, the more accurate the data are. Unfortunately, Alexa doesn't provide information on the number of Alexa Toolbar active users (it could be something like several millions). Second, concerning Google Analytics, the largest potential impact on data accuracy comes from users deleting or blocking cookies. Without cookies being set, Google Analytics cannot collect data. Plus, many ad filtering programs and extensions (such as Firefox's Adblock) can block the GATC. This prevents some users from being tracked, and leads to holes in the collected data.