- Lack of ownership of the statistics - Google owns the data.
... As for the ownership issue, this is a
bit paranoid IMO.
One problem with it is that we can't even access the raw data. We had a use case this week where we wanted a visitor map for an executive presentation. We needed to get more flexible with how the visitor map is displayed (wanted to view the map in Google Earth plug-in). In GA, you can't. You take what they give you. You can see a map of how many visits came from each city, but you can't export a data file of cities and number of visits, to run the data through other tools. So, paranoia aside, there are significant limitations on what you can accomplish with GA.
However this is not a problem if you use Urchin, the self-hosted version of GA: you can export the data and do what you want with it. (And the exported data is richer than the web server log's, as it includes some analysis already.)
Since Piwik is open source, and pluggable, I imagine you could enhance the visitor map plug-in any way you wanted to. And export whatever data you want.
Whether this limitation affects you depends on your needs, obviously.
Update: I've now looked at the GA Data Export API, and it turns out that things you cannot do through the UI (as you can with Urchin), you can do with this API. It does look like you can export the visit data I was talking about, via a feed (although there are daily traffic caps on those requests). So sprinkle salt heavily on what I wrote above.