The problem was, that for no reason I can pin down, AirDrop was never in the sidebar. Selecting it from the Go menu or via shift/command/R only opened a finder window which displayed available drives, and double clicking the AirDrop icon would open the pane. It was always like that on both machines, but just stopped today on the MB. Jim had me check AirDrop in the finder prefs, which placed it in the side bar, so now, regardless of how I access it sidebar, Go, keyboard shortcut the pane opens immediately.

Just one of those things that hide in plain sight.