This is kind of a grey area, however, I've been on cross-fleeted flights, so I've learned how it works.

It basically depends on the hub from which/to which the flight goes. A NW 747 going HNL-ATL as DL802 is considered a DL flight. In this instance, you list with DL and are upgraded for free, but behind DL employees even though it's a NW A/C. A DL 767 going from SEA-AMS as NWXXX is considered a NW flight. Listing would be made with NW, NW employees will be upgraded for a fee, and DL employees CANNOT upgrade, even though it's a DL A/C. Now if that exact same A/C turns around in AMS and heads to JFK, it will be operating a DL flight with DL rules.

It comes down to the hub, if the flight is headed to DTW, its a NW FLIGHT regardless of what the captains ID says. If the flight is headed to ATL, it's a DL flight.

Hope that helps.