One picture that sums it up for me is the Insights functionality Facebook can give you:
That’s not for my app on Facebook, that’s for clicks on Like/Share buttons on this site, right here. You can drill down further and get clickthrough ratios, likes for individual pages, etc… Along with a whole bunch of other detailed information.
Because the “site” is separate from the “App”, I can get similar stats for likes on my Facebook Page (really an app) and such too.
BTW, if you’re using SFC and haven’t enabled this sort of thing, then it’s really easy to do. You can do the same thing without SFC, it’s just that SFC makes it easy for you by putting all the proper header codes into your page to make it work seamlessly.