I have been in both a local and a national sorority. I joined a local that later became a chapter of AEPhi.
As a local, you get to make your own rules without being answerable to a national. That can be abused (read: hazing) but isn't always, and wasn't in my local's case. You also don't have to pay national dues; while my roommates were forking over $600+ for their pledge semester, I paid about $100.
As a chapter of a national, you have a lot more support. You don't have to create your own ritual, find a philanthropy to support, figure out your own rush events, etc. You can also go to new places and bump into sisters, which is considerably less likely if you're in a local.