A few answers...
First off, you're comparing apples to oranges by comparing statcounter and a logfile analyzer. One is JavaScript - run by browsers with JS enabled. Spiders, visitors who decide to turn it off, and some old browsers won't ever show up in a JavaScript tracker. On the other hand, logfile analysis only shows requests, so people hitting the back button show as another view in a JS solution and don't show the new view on a logfile stat package. JS and logfile won't ever be the same, no matter how much they work to get similar results.
Second question was about Alexa. Well, that only shows visits by people with the Alexa toolbar installed. I personally don't have it installed. Nobody that works here does (here or at home). That means that our visits aren't counted by their system. However, when we see visitors on our site from Amazon, they always have it installed. The fact that their employees all have it says that their numbers are naturally going to be higher.
It's a measure, but not the best. Most certainly something you can look at, but realize that it doesn't show you any facts - just some sort of a number as a guess. You could also look at the numbers from trustgauge, but that has the same problems.
Brian.
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