As far as accuracy is concerned, I would think your best stats would come from Webalizer, or any other server software that draws the stats from your raw logs.
Offsite counters/stat packs such as Hitbox don't allow for this, and many of the cookies/installation files are destroyed and/or blocked by various anti-spyware programs.
So if it were up to me, I'd say "if Webalizer looks pretty enough to you, leave it alone because it's probably right."
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