The statistics of a program that analyzes the server logs are quite different from those computed by phpMyVisites. Which should I trust?

Statistics based on the server logs (AWStats, Webalizer, Analog, etc.) are less precise than statistics based on Javascript image calls (like phpMyVisites statistics). Very often, it happens that some visits are not recorded in the server logs. On the other end, log analysis tools do not always support the many IP addresses one single visitor may have.
As for Webalizer, the statistics it computes are not reliable since the software is quite old (the last version was released during 2002 summer). Therefore, a lot of the problems that appeared recently are not dealt with (changing IP addresses etc.). The software gives figures for visits much bigger than they really are (sometimes twice as big).