I'm not sure how accurate Awstats could be, but I would always suggest run your own stats scripts after testing and finding the right one. Awstats is usually attached to Cpanel and, if you switch to a host without it, you will not be able to keep a coherent analysis of your charts flow, as per Google Anayltics and others, they might be or might not accurate, but I don't see the point of using third party providers when you can run it on your own. Unless, of course, you are short in webspace, bandwidth or perhaps not enough PHP knowledge to install it and keep it running.
i would believe Awstats is mroe accurate as sometimes you might have the ga code on the bottom of your page, and people might leave before it loads.
Awstats is accurate in what it does. But its definitions are not as you expect. For eg: 1. A same person who visits your site with two different IP addresses is counted as two unique visitors where as cookie trackers will count him as only 1. 2. A hit is not same as a pageload or visit. Hits are the no. of files requested from the server. Eg: If your homepage has 9 images, then a single visit generates 10 hits. 3. An IP address whose visits are not apart than 12 hrs are taken as the same visit(I am not sure about this one though). http://www.totalchoicehosting.com/forums/index.php?showtopic=4639 http://www.webmasterstop.com/47.html [This one seems down, but I had it bookmarked earlier]