The aim of the measure of 'unique visitors' is to help find out how many individuals have visited the site - i.e. how many new visitors the website has attracted. It might sound easy, but in reality, it is not all that scientific.
What you'll notice about these tools is that they both define "unique visitors" in different ways. In fact many log analysis tools do differ in the way they approach the situation.
AWStats according to the documentation defines Unique Visitors as:
'Unique Visitor' - These are the total number of visits by a unique IP address. In summary AWStats simply calculates a total for this from the log files.
Google Analytics on the other hand has two metrics, measuring both by percentage:
'Absolute Unique Visitors' - tracking each user's first visit, and;
'New vs. Returning' - by tracking subsequent visits
'New vs. Returning' - by tracking subsequent visits
In summary, Analytics uses cookies and sessions to differentiate returning visitors. There are advantages and disadvantages of both approaches and any can result in undercounting and over counting, as both IP and cookie counting can have inaccuracies. As a result, you'll sometimes find large discrepancies between the two sets of results.
Both these tools will give you monthly and yearly totals and averages, which can be quite useful when presenting a report to management on how your website is going. Ultimately, however, there isn't really a definitive way to know if the same person has not visited your site before. So we just use some educated guesses to determine numbers for visitors that are "unique", and use both to get a feel for some common ground.
While I have a personal preference for the Google Analytics style of presentation, I use both types of stats tools to analyse trends.
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