Despite both programs appearing to give the same information, the user statistics and viewer data can vary wildly between Google Analytics and AW Stats. This is because both programs gather their information in a different way, and for different purposes.
AW Stats gets their information from the raw backend of your website and is the most accurate for finding the number of visitors to your website. If you have posted a new blog post or added a new product to your website, and you want to know how many times that link or page has been clicked on, AW Stats is going to be the best way to find out.
To make things simple, think of AW Stats like a census, whereas Google Analytics is more like a focus group. Just as the names imply, AW Stats is for finding your viewer statistics, and Google Analytics is for analyzing your viewers.