Piwik allows us to have control over our own data instead of using a third party service to handle it for us. With it, we can access the raw analytics data if we want or write new modules to present the data in a new way. Piwik truly gives you full control and it's easy to implement.
I have used Google Analytics, Site Catalyst, and Awstats as well as Piwik. There are some features that Google Analytics and Site Catalyst have that aren't available currently in Piwik, but most of those I don't currently need. Owning my data is more important to me than bells and whistles. Piwik is a modern analytics package that beats old school Apache log parsers like AwStats hands down.
If Google Analytics is too complicated for you, than Piwik is probably not the best for you. If you are going to use Piwik like Google Analytics, at least you have control of your data. So I would recommend that. But if you are really into the stats on your website and don't mind getting your hands dirty, you can find no better analytics platform than Piwik.
Well, now I am just simply used to using Piwik and I haven't run into a competing product lately that has tempted me away. Upgrades are easy and creating modules for Piwik isn't that hard, so I will stick with it.