I like your idea "- Change the checkbox in a list where you can choose Webalizer or AWStats, and generate the Statistics by the chosen program to /stats" and "- Add an AWStats checkbox, and leave AWStats in /awstats". However, to expand upon this if someone only wanted to choose one stats program they could define where it is generated.
Ie. If you wanted both then one could go in /webalizer and /awstats or any two directories you want.
I also like the simple idea that I choose which engine I want to use and it is dumped into /stats. This I'm sure would be the simplest to enable from your side as well.
Nice work on the awstat function by the way.