There is a new Facebook Pages Manager app. The tools in it are better suited for the business/fan pages.
I've no experience with it, having only a personal site; but I recommend you get the new app and login/use it for your business site, and use the standard FaceBook app for your personal site.
Edit: Oh crud! Looks like it's an iPhone app.
It should work on the iPad, but won't look very good. A less desirable alternative is to use Safari to access one of your sites and the FaceBook app for the other. Sorry.