Well, the figures themselves for Facebook are pretty impressive to begin with. Taken from their statistics page :
With 350 million people accessing Facebook from a mobile device, it may be easier to develop for their platform versus creating a mobile edition of your own website/app.
With the social aspect of Facebook, they provide a ready environment that will help with word-of-mouth and also potentially with creating a viral effect.
Bottom line, it should be easier to promote and grow on Facebook, versus an independent website standing alone out on the Internet. Also, there's no reason you can't use the app to drive traffic to other web properties, should you have that standalone site.
It all depends on the nature of your application in the end, but if it can fit on the platform, the benefits are definitely there.