Google Analytics is great for finding out where your traffic came from. It's pretty good for showing event/flow conversion. The event system is maddeningly limited (you only get three fields to work with) and you can't push user-level attributes over for later ad-hoc use by analysts. Great marketing tool, but it's weak sauce for product management and analytics.
Mixpanel allows you to send over any mix of key-value pairs per event. You can segment by any key you provide, and you can pull down all the raw data later for your analysts to dig into. However, Mixpanel defines "conversion" as "a subsequent event that happened one or more times within 30 days." I suppose this works well for some types of businesses -- just not the ones who are really serious about making money. If Mixpanel had any concept of a session it'd be fantastic; as it stands, it's a very serious flaw.
I will say, my experience with the Mixpanel support has been truly outstanding -- even though the tool doesn't do everything I necessarily want.
The implementation I've been happiest with is to run both GA and MixPanel.
Marketing: Google Analytics. GA quickly becomes unusable if every group piles on their own requirements.
Product Management: Mixpanel
Reporting and Analytics: Pull down raw Mixpanel data via their export API, sessionize it, and make that data available for your data geeks (raw) and for your KPI reports (cubes/views).