Jay,
It's a Facebook restriction that you can't have two FB applications running on a site at the same time. They only allow you to enter the AppId to initialize the Javascript once. Two times isn't possible. Additionally, when the "Login with Facebook" button is clicked, Facebook is 'told' which extension should handle the user after they've authenticated. It's not possible to have Facebook notify 2 extensions that authentication has occurred, so only one (JFBConnect or the Classifieds) would be able to log the user into Joomla, create their account, or update their profile. Not both.
With that said, if there's some very specific separation you're looking for, we may be able to help you pluck the best parts of JFBConnect and the Classifieds extension for your needs. Specifically, you mention Canvas apps.. if you need just the Canvas App views, which also include the new Friend Inviter and App Request system, of JFBConnect, but want the Classified component to manage authenticating users on the site and other social buttons (like, comments, etc), that's probably do-able. However, if you want them both simultaneously always working, that probably isn't.
Hope that helps,
Alex