Question: Why would you want them to do exactly the same? If they would do exactly the same thing to me it wouldn't make much sense to have both.
Google Analytics counts the number of visitors, Statcounter counts the number of clicks/page loads. Anyway Statcounter also shows the number of visitors in addition to the clicks as you see in the graphic you find on the project page (Green: page loads/clicks, Blue: number of visitors).
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The number of visitors varies between Statcounter and Google Analytics because of the time setting. If a visitor leaves the site and comes back two hours later Statcounter counts it as a new visitor, I don't know what time delay GA uses but that explains the difference.
Statcounter, Project settings
Idle Time Between Visits:
This is the amount of time that needs to elapse between pageloads for a pageload to be considered part of a new visit.
How I see it: use Statcounter for the clicks. Google Analytics for the visitors. Two different data which tell you different things.
To keep Statcounter from counting your visits go to Statcounter, Blocking Cookie (from the menu at the top), Create blocking cookies.