Panels creates different pane number for any mini-panel inside a panel-node
I recommend using the pane configuration itself under CSS Properties to provide semantic class names for each pane. Create some sensible defaults for .panel-pane and extend it by adding classes. Eg users or themed-list list-striped. If necessary extend the concept using CSS ID's. But I think that's taking it a little far.

If that isn't enough then sometimes I create a custom panel layout with additional wrappers, classes and regions.