I personally prefer to use HTTP log analysis software. Gives more power to me and doesn't contribute to large companies tracking everything.
Unfortunately, though, finding a good log analysis tool is very hard. Finding one that can beat Google Analytics is even harder. I'm still using AWStats myself, but I can't say I'm really happy with it.
isn't that because there is inherently less data in http logs? Google Analytics use cookies and Javascript to track more data on users. There's no session data in http logs.
You're partially right. Log analysis will require some more tricks to get the relevant data, but there's still a LOT more that a log analyzer can do than AWStats or similar projects do. I believe it's perfectly possible create a log analyzer that can compete with GA.
(Then there's also another trick used by some log analyzers: Putting a bit of Javascript code on each page to request an empty image or AJAX call that generates a log entry with tracking info. But I'm sure that there's a lot that can be figured out even without something like that.)
Unfortunately, though, finding a good log analysis tool is very hard. Finding one that can beat Google Analytics is even harder. I'm still using AWStats myself, but I can't say I'm really happy with it.