Piwik Analytics vs Google Analytics : Why We Use Google Analytics
The question of using Google AdSense and Google Analytics is not exactly the same. Google AdSense frankly tracks the fraud clicks and real clicks. We use Google Analytics mainly as an old habit of using a free analytics software. We often forget that, the theft and Spyware activities by the Governmental agencies is the truth. If you are looking for an interface which looks like Google Analytics then you might use Open Web Analytics not Piwik.
You can read two more resources on the same topic :
If you are in assumption of unknown fear of getting banned by AdSense, we would suggest you to change your way of earning first. From AdSense, not only you are earning, Google is also earning. The fear of stolen privacy should be of more concern. Piwik is very easy to install, actually like WordPress or any PHP-MySQL software like we described here.
Piwik Analytics vs Google Analytics : From Technical Point of View
From Page Speed optimization point of view, Piwik is actually better as it by default will be installed on your own domain. The scripts will be served from consistent domain, you can fine-tune the loading of the script. We can not stop using few things which are known to steal data of us and the users, but we should definitely opt-out where there is option.
Basic data which are related to SEO can be found from Google Webmaster Tools. Google Webmaster Tools is much of importance than Google Analytics. Practically you need to know few basic analytic stats which Piwik does efficiently. Recommended article to read for increasing awareness about Privacy in Cloud Computing.