AWStats is most accurate because it uses server access logs. So it tracks any kind of hit that your server gets from anything. Analytics is a piece of Javascript code... if it's not run, it doesn't work. People with Javascript disabled won't get tracked.
Use both and take average. This is what i personally do. Most of the time awstats registers much more "hits" (sometimes not real visitors) because the stats are coming from serverside logs.
I use piwik for all my sites and it works greatanyone using Piwik ?
it has similar interface to Analytic and pretty nice since all data store on your host and it totally free
Well, analytics leaves footprints.It tells google what you are doing.For example if you have multiple sites/ blogs and you are doing some shady things on them a good idea is to not have analytics on .
If what you're doing is squeaky clean then sure, analytics is the way to go.