depends entirely on how you configure each piece of software.
Webalizer counts a "visit" as an IP seen in X period of time. I believe 8 hours is the default for this? I could be mistaken.
That means, if I load your site at noon, and then at 9pm, I am counted as two "visits". This makes logical sense to me, at least. To calculate visits from log files, you have to have an arbitrary cutoff of "how long of a period of inactivity re-sets the "visit" counter for this IP?"
I would assume AWStats has a similar setting. Make sure these both match, and re-run stats. If they are not within a couple visits of eachother, then obviously one or the other (or both) is calculating wrong
-Phil