ElFroggio
Why do you use Affa, what is wrong with using the standard server manager workstation or admin console backup to local USB, then installing sme OS on the new server, & then restoring from the backup, & then reinstalling the awstats (& other) contrib(s) ?
That is the recommended way & AFAIK includes all data, except by default any installed contribs (& /opt unless you manually specify it with a custom template).
Where is the awstats data stored?
Last time I looked it was in the admin users home folder.
How can it get backed up with affa?
It should be backed up & restored, unless something is wrong with Affa (& there are a number of suggestions of possible unresolved ongoing issues & bugs with Affa) or maybe you have followed the procedure incorrectly or done something else incorrectly.
Did you reinstall the identical awstats contrib after restore of data ?
Are you using the same domain name that awstats was originally monitoring ?