For us at STL, it doesn't really make much of a difference. Runway 6/24 isn't used all that much, but when it is, we typically only use 24 (operations on runway 6 are strange and only seem to serve to confuse the TRACON, though we have been known to use it), so when we tell someone to cross, we usually say to "cross runway 24". Almost all of our regular pilots know the route anyway, so they don't question it.
When the runway is inactive (such as 6/24 is most of the time for us), if the tower controller keeps the aircraft, he won't coordinate the crossing with Ground, even if Ground owns it. We consider it the same as using a taxiway, though we still call it a runway (example: "Taxi to the gate via Papa, Quebec, Charlie; cross runway 30L). Without the actual words "Cross runway XX", a pilot is not authorized to cross a runway, active or inactive. The only time we appreq a crossing is when Ground needs to cross an active runway.