How do Alexa and Compete get their data? which one is better?
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From my own experience, I think Alexa is more reliable, because its user database is bigger.
It's not really that easy to compare, because they deal in different metrics.
Looking at Compete's Unique Visitors for a site that i'm involved in, they give an average of 4,000 unique visitors per month. Google Analytics for the site average 180,000 unique visitors per month.
For Alexa, the metrics are all expressed as a percentage of global stats, or " unique pages per day" -- things that no one else uses, so there's no way to gauge the accuracy of the stats.
However, i believe that the problem is the small, US-centric sample which penalises non-US sites (FYI, the site i'm talking about here is for a business in South East Asia).
Moreover, looking at the textual information that Alexa presents, i'm concerned that it's several years out of date, which makes me doubt the efficiency of the system. According to Wikipedia:
The Wikipedia article is a good read, as it talks about the accuracy of stats.
Final word: trust only verified stats!