I want to tell you all about Piwik. It's great analytic software (I prefer it over Google analytic because it can give you live stats and it's easy to see day-by-day reports). I also like it because you install it on your own server and everything goes in your own databases.
They're both pretty much the same - but Piwik gives you a live visitor view (in an Ajax window). I just think it's easier to use because I like to see my traffic for Today and not for a month (like a Google Analytics default). It's just a different interface. For example you can make it show stats to the public.
They offer a number of features that Google doesn't. For example, they're getting big in Germany because Piwik has a feature to conform to their new privacy laws.