Facebook Insights shows demographic details and interactions on your pages BUT limited to show information of fans only. It is far less sophisticated and comprehensive when compared to the free Google Analytics.

One of the limitations of Facebook Fan pages is that you can only run limited Javascript on it and Google Analytics needs Javascript code included to correctly track visitors. We have successfully managed to get ALL functions of Google Analytics working on our Facebook fan page (including visitor statistics, traffic sources, visitor country, keyword searches with all other powerful reporting & maps overlays etc).

Article From: http://www.webdigi.co.uk/blog/2010/google-analytics-for-facebook-fan-pages/

webdigi.co.uk is a web development company in London and who focus on developing web solutions for our clients globally.