I've used Piwik for years and it is incredibly simple to use and set up but this post makes it much more complex than it needs to be. In all honesty, it's just as simple as setting up Wordpress. Drop the Piwik folder on a server somewhere, run the installation (connecting to your database and if I recall correctly you don't need to use the root user, just a user with sufficient privileges), and you're done.
I want to love Piwik, and I do like it a lot, but I do have some problems. Piwik gets slow after a while. This may have to do with the server its running on partly but over time the software will slow down especially if you try to pull out somewhat longer date ranges.
It isn't as pretty as GA. I know this is petty and that its themeable but the UI was important to me. Keeping it up to date and maintaining it was also something that requires vigilance. It isn't hard to update but you have to make sure to check for updates. Sounds simple but you'd be surprised how lazy one can be. Also, integration with Webmaster Tools isn't available which is kind of a bummer.
On the plus side there's very little that GA offers that Piwik doesn't. There's even a great mobile app which GA doesn't yet have to my knowledge. You can monitor multiple sites on different servers using a simple JavaScript snippet just like GA, and it breaks down the data in just about every way you'd want.
In the end, despite really wanting to use Piwik long term I wasn't able to do it. I don't see a problem with using Google Analytics for tracking purposes. Google has the power to abuse the data they collect but I trust them not to. I'm not running a site where visitor privacy is a big priority. If I were running such a site I'd reconsider this position. But from an ethical standpoint if it's somehow not okay for Google to collect tracking data on your visitors (and promise not exploit it) why is it okay for any of us to use Piwik and collect that data ourselves. Google has far more data that can do far more damage but they also have far more resources to put into security than most of us. I can take a pledge not to exploit my user's data but Google does too? I know I can trust myself but my users don't. My users might even prefer that if I were to use analytics software that I use software that comes from Google, a name they know and trust, rather than me, a guy who they know a little bit but doesn't have a reputation that can even remotely compete with Google. To me, that's the more interesting aspect of Piwik. The question of why running your own anaytics software is more ethical than using Google.
Edit: When I said I wasn't running a site that made visitor privacy a priority I was excluding the site I run that actually does make user privacy a huge priority. I'm aware I look like a hypcrite now and I think I might actually spend some time thinking of whether or not to switch over to a self-hosted analytics solution for that site. I'm still not sure that a self-hosted service is preferable in my case but I'm open to the idea.