Since I can’t see your server logs, I can’t say for certain what the discrepancy may be attributeable to.
Certainly, one of the big differences is that Piwik is bot-resistant by using JavaScript (and server-side filtering).
Other comments:
if you use javascript: links, Piwik ignores those. If you want to track them, you have to call trackLink() from your javascript.
if you use onclick() handlers which return a value; any value can cancel event bubbling/propagation in some browsers; due to the undefined order in which click handlers may be registered, this could prevent Piwik’s click handler from running
I just took a quick look at your site, and actually, you do use 1 and 2.
Um…the URL to sample-stats.txt is broken. I tried a couple of variations in case you typo’d. You’ll see those attempts i your logs.
The 30 instances of libwww-perl suggests your site is being crawled by bots/scripts. The majority of bots don’t execute JavaScript and thus, would not be tracked. Smart bots (e.g., using HtmlUnit) or scripts that spoof the User-Agent will be harder to detect.
As for 1,2 - these don’t account for much traffic and links like these are being clicked maybe 1-2% of times. Most traffic produced by plain html links.
Additional problem is wordpress blog - piwic stats show visits 10 times less than wordpress counter. Blog is here Влада і Соціум - with piwik plugin activated.
Also - mediawiki own counter shows 3 times more visits than piwik.