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They're measuring completely different things.

Number of raw searches != number of users

That said, Compete numbers have always been hilariously random.

The best numbers I've seen consistently are from Google adplanner: http://www.google.com/adplanner/

That might be true for your site, but for sites I have intimate knowledge of while freelancing in the analytics space, Compete has always been the closest. Except for their search analytics, that is so hilariously bad they should split test not showing it on the site.

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