I'm just trialling OWA at this very minute, but a few key differences:

OWA's interface is much more professional.

Piwik's codebase appears to be a lot more stable.

Goals in Piwik are pretty basic: for example, you can define a page that triggers a goal, but not a funnel like you can in OWA.

It's easy enough to trigger a custom action in Piwik (e.g. logged when someone clicks on a PayPal button - just add an onclick="log me code"), but the display leads a lot to be desired. OWA seems much more polished in this regard.

OWA apparently has click heat maps, something that Piwik lacks, but I'm still trying to find them in the interface ;)

Those are my initial impressions. In short: OWA has the features, but Piwik's code is stabler.