If your store can move directly to your facebook page then you have removed a single click from the user flow. Additionally your visitor can shop in the confort of their own facebook visit and not interrupt chats and games that they have going. Moving your store to your facebook page is a must have move for your eCommerce initiatives.
Using a service from wishpond I was able to automatically synch my items and inventory with my shopify service. It takes a little while for the initial synch, but if you have an issue pop a call into their support. They were super helpful and cleared things up right away. The initial synch is free, but if you want to manage inventory and change things you need to convert to a paid account. Certainly worth the 20 minutes of time to take it for a spin.