I keep the tracking code in the same place for both services. I review my PIWIK numbers every day. Today, I went to Google and looked at my numbers there. Google shows about 20% more aggregate visitors (repeats + uniques) for ever single period. Since the PIWIK code and the Google code are on every page in exactly the same place, it means that both services get the same number of calls. I verified with Firebug that both are called every time.
What is the reason there is such a large difference?