My hosting provider includes AwStats and Webalizer in their package.
I have a site with Drupal on the main page. Recently I found out that Google Analytics provides support for integration with Drupal through one of Drupal's add-on modules, that is I do not have to put Google Analytics code into each and every page of Drupal. I am tempted to install it.
I want to ask if there is any difference in the information provided by AwStats and Google Analytics? I can't disable AwStats and Webalized. Will adding Anylytics put extra load on my site?

Yes, there is a difference between AWStats and Analytics. AWStats will provide you with more exact statistics in terms of a raw data. Analytics on the other hand will provide you with nicer interface for browsing through collected data.

Both systems provide you with user's geo info but I believe Google has more precise data regarding IP addresses origins than AWStats has. Analytics is meant to be used for tracking web pages only while AWStats tracks other things like images and bandwidth as well.

If you're using Google AdWords you can combine two of their services.

Putting Analytics code to your website will not cause any overhead to your server. On the other hand, users visiting your site will be contacting Google's server for each page they visit. That overhead is negligible.

Since Google Analytics is a javascript widget it is only triggered by users running Javascript, so it won't tell you about the other visitors. AWStats uses your server log files so it sees everybody / everything that loads a page. That includes users who have turned off Javascript or are using browsers which don't support it. They might even be using a plugin to specifically block GA. Users like that may be a minority but with GA, you'd never know they exist.

Log file analysis also includes bots and spiders which you may find interesting to monitor.

Any idea what's the percentage of users without javascript?

Not sure, I have seen figures around 5% (e.g. http://www.w3schools.com/browsers/browsers_stats.asp) but it'll depend on what kind of audience your site attracts.

According to Google, analytics also requires images and cookies to be turned on, so the number of users which don't trigger the tracking scripts may be higher than that:
http://www.google.com/support/googleanalytics/bin/answer.py?hl=en&answer=55610