Differences in numbers: piwik vs. awstats vs. google

I just searched the forum for awstats and found this topic - maybe someone has an answer to this now?
We’re facing the same problem: way less visitors in piwik than awstats shows. Example for a day in June:

Piwik (0.63): 52 visitors
Awstats: 302 visitors

I read the FAQ but even thinking of all the points mentioned in FAQ#50 I think the difference is too high. Robots etc. are exluded in the Awstats numbers.

Also we’re running some ads with adwords and the keywords of some clicks that were generated are not shown in piwik (when looking at the keywords in piwik), but here piwik seems to drop way less visitors (coming from google) than in general.

Any ideas what we could do or what the problem could be here? Or are the 302 visitors of that day just completely wrong and over years we thought we had a lot more visitors than we actually do?