I've did this before too and it was honestly one of my best RPG experience ever.
I did this with my homemade RPG system in a futuristic setting.
There was 2 GMs, and 2 groups made of 3 players.
The first group were the "bad guys" working for some influent criminal group called RedDemon. They (the players) had to take hostage the president of the city to "negotiate" with the clan's chief to give them power over the city.
The secon was the "good guys". They were working for the law officials of the city and they learned about the RedDemons activities and try to stop them.
Each part of the scenario was written in two parts, the first if they succeeded the mission, the second if they failed (giving them an alternate objective), and that for each of the group.
Each group was in a different room, but each time one group was going into a new place, the GM told the other. Maybe some RPG God was with us this day because it all worked very smootly. Each time the "bad" group left a place after their evil doings, the "law" group had accumulated just enough informations to know were the bad were to hit next and entered the place just minutes after the "bads" left, making them always on their tail.
You can cheat that of course, because the two groups shouldn't meet until the very end. At the least, if they meet, the "bad" guys should have finished their job there and should try to escape the "law" group instead of trying to kill them.
To make things more clear, here's some example of what happened.
The "bad" group tried to break into the president's room (in a hi class hotel) to capture him. Unfortunatly, there were some heavely armored and armed guards there, so they sneak up and was forced to hide in a random room when a patrol passed by. The resident was about to call the security, so they had to kill him before he warns them. During this moment, the law group went to interrogate some criminals in the slums, were told about the plan to capture the president, so they went to his appartment in the hotel to see if all was okay. They checked the president's room, all was okay, but they found along the way one dead guard, so they investigated and finnaly get to the room were the bad guys were hiding. [The timing was perfect, the other GM told me just seconds after they killed the man in the room that his group knocked on the door of the room just next to the president's to see if anyone saw or heard anything]. Panicked, the "bad" PCs had to hide their weapons and the body in seconds before opening, they tied the body with some rope and trew it out the window to hide the corpse and they somehow taped their weapons under the table to hide them. [For this scene, we all gathered in the same room]. The law guys interrogated the dudes, they looked around to find some evidences (they even looked out the windows but didn't noticed the body tied up some floors below and moved the table to climb on it to check the air ducts, wich gave some chills to the "bad" guys who knew their guns was taped just under the table).
Well, as I said, maybe some kind of game god was with us, but all went very smooth and very intense and ending up in the final scene where the bad guys hid in an appartment and the law guys knocked on the door (it was the RedDemon's chief ex-girlfriend's appartment, wich the law guys found out that could be a good hiding place) and the bad guys had no escaping route, so they just opened fire at them from behind the door, wich led to the final confrontation. Law group was winning the combat, but one of the criminal group PC was a pilot and electronically called his airship wich arrived some rounds after the start of the combat, wich gave them some way to espace... that led to the final chase scene where the bad guy's ship was badly damaged and they crashed unto a building, having only 2 of the PCs surviving the crash and escaped on foot, badly injured.
To be honest, if I would have played this game again at some other time with other players, I'm sure I couldn't reproduced this perfect gaming session, but having 2 dms with 2 groups confronting each other (but not physically until the very end) was the greatest RPG gaming ever!
If you search on line for "GMing deckers" (as in the decker class from shadowrun rpg) you should come across a lot of ideas you can adapt to your situation. Some ideas off the top of my head...
