For instance:
1.) Different handling of media by the military. Vastly different press releases from the MoD, RN, etc. which swiftly ramped up to unveiled threats of death and destruction.
2.) LOTS more military shows-of-force and manuevering; heightened states of readiness at the major airbases. When Al Udeid goes to FPCON Delta / MOPP 2, something is up.
3.) An attempt to accually use the situation for gain; calls for stronger forces in the Gulf, etc.
4.) Primary players drawn from "special" military organizations. It seems that all the kidnapees were from perfectly ordinary backgrounds; no one has come out with information that they were associated with the Special Boat Service, the Royal Marine Commandos, SAS, etc.
5.) Better behavior from the victims, tougher behavior from the negotiators!
Aside to number four: If on the other hand, your kidnapees were just pawns who had no idea of their position but were being used nonetheless, I'd expect less diplomacy and more shows-of-force. Look at the Jessica Lynch operation from OIF for a paradigm; she obviously wasn't set up to be a propganda coup, but when the opportunity arose, low-light video cameras were on hand to record the rescue.