AWstats is easy to manipulate and when buying/selling sites not very trustworthy. I wouldn't buy a site on Awstats, unless it was something extremely spectacular. Google Analytics is free as long as you have fewer than 5 million page views per month, it's easy to understand and to implement it. It's well known, so anytime someone says "I haven't installed it" I just see it as a bad excuse for trying to hide something fishy. Never buy such a site, if seller is good and honest and have any interest in site at all, they themselves will install Google Analytics.
If the prospect buyer will want to see the analytics or awstat, then show it. It's just a part of convincing your buyer to buy your site.
Google Analytics is much nicer than AWStats. I've found that they're Analytics is much more detailed and accurate (and nicer looking) than AWStats.
i think Analitic is better than AWstat, Google analitic show you real traffic and more information on it.
Google Analytics is a tool which allows you to see where and how traffic comes to your website. For instance, when Google Analytics is added to a website, within your Google Analytics account, you can view and learn a huge amount of information about your website, such as referring traffic and keywords searched to land on your site. To add Google Analytics to your website, you will need to sign up for a Google account. Then Google will generate a code which you will need to add to the code of your website, generally in the footer area. There are also advanced settings which will track conversions, Google ads and lots more. So i would choose Google analytics as the best tool for knowing the status.