Does Awstats and Webalizer really provide more information than what Google Analytics provides? If not is it a good idea to disable them?
I wouldn't use either and I haven't been a fan of even having awstats since they became an easy target for hackers. I'd stick with google analytic, ment or woopra. Those will give you enough info on your site.
"There is no exploit nor hole known by AWStats team on this version or on higher versions, so AWStats 6.9 and higher are safe."