I don't think you can use just one. A lot of people like myself block the analytics cookies. I have had problems with AWStats too -- recently some log entries have caused it to barf and quit parsing the file (they have no referrer or user agent string, and come from a site monitoring service that scans for vulnerbilities -- I may have to hack AWStats and submit a patch to fix that).
I use "visitors", but Google Analytics is getting better.