I didn’t see a clear winner after poking around with the three tools so I decided to try all of them together. I’m really glad I did because this is the comparison table (based on my experiences from above):
Mixpanel KISSmetrics Google Analytics Tracking Events Great Poor Poor Measuring Funnels Poor Great Average Analyzing Traffic Poor Poor Great Real-time Yes No No Setup Difficult Moderate Easy
They’re all great at different things! And since what you need to learn will change over time, you really need more than one tool in the long term.
Arthur Klepchukov has posted a nice comparison between Mixpanel, KISSmetrics and GA. While I believe that GA can be quite good in everything, with a little bit of Mixpanel sauce, it's still a decent pros/cons table to consider.