ah, I see what you mean now. But while that would be a problem, it could probably be addressed to some extent. The number of lives could be adjusted, weapons, we could also always give the attackers disguise kits or invisibility watches too. If the attackers have a disadvantage, there's probably going to be some way to balance it out again.
Also I gtg do something, I'll be back in a little bit.
There is also 1 more reason why lives are inferior to time. You join the game and then wait ten minutes for that idiot still at the spawn to die or get kicked. Or you have to wait for the guy who is actually playing, but will take forever to win or lose.
Some advantages of a timed game:
You wouldn't have to deal with idiots not doing anything.
Cooperation and emphasis on stealth could be greatly enhanced. Imagine if each room had some sort of laser security system where if you walked through a laser, you would be detected and it would tell all of the guards. Normally this system would be easy to avoid if you were cunning and skilled, but a shoot-em-up type of player would walk right through it and waste his time. This system could also be used for cooperation though. Lets say you have the majority of attackers enter the room and trip the system on purpose. Being that they are a huge group, thy could hold of the guards for quite a while. While all of the guards are drawn, three or so skilled players could run around the compound and finish the mission.
Lives are really tricky. If all teams have 1 life, then it is just too quick and the victory goes to those with the quickest trigger fingers. No stealth would happen, the attackers would simply try and wipe out the guards. This would inevitably result in a weakening of the attacker weapons until it would be impossible for an attacker who was trying to be stealthy to ever get past a guard. If you give too many lives, it can take a long time. You also end up with people who are unlucky being removed from the game and then quitting because they hate waiting.
If you have time, no one will care about trying to kill the other team for wiping them out, because it is impossible. You could also just make the respawn time larger in order to discourage wasting a life.
Also with a timed game, you end up with a lot more of a havoc type game. Guards are running everywhere trying to keep up with all of the unskilled players, while more skilled players can sneak past these worried guards. It creates a lot more of a mental feeling of infiltration.
Over all, lives will end up maximizing the abilities of skilled players, encourage sneakiness, and encourage teamwork. It will also prevent the problems of afkers and those who wish to win by killing everyone.
UNRELATED to my argument for time: Another important thing to do would be to get rid of kill messages in the chat.