For fully-filled steel decks, from what I've read, I think it's mostly an ease-of-installation issue. You can have the decks ready to go and drop them into place versus having to set up forms and wait for the concrete to cure with a conventional deck.
For partially-filled decks, there can be a significant reduction in dead weight which can be a major consideration on older structures. I've seen where they filled in cells in tire paths for improved traction. In the case of the bridge over the New River at Thurmond, WV, some cells in the shared vehicle/pedestrian portion were also filled in during a recent rehab to make it easier for pedestrians to cross the bridge.