1 person gets the mission.

Everyone can warp with them and help them complete it. When you turn in the mission, i BELIEVE that everyone who is in your gang will split the reward (I know the reward is split I am just not sure what the determining factor is, but I think its everyone in your gang). So if you have anybody with mission bonus skills (Which would be smart if youre going to mission a lot) you want to have that person taking the missions in order to increase the bonus.