They would be seperate story's that meet at one point
I don't want to get to know a character just to have him die, and then I especially don't want to play as the guy who just killed me, he's the enemy.
The way I see it is for example, you'd begin as a street thug kinda guy who is moving up in the ranks of his gang, he sets up a meet to buy some drugs from a mob, something goes wrong, there is a gunshot outside, the Mob boss has been shot, you see one of mob chasing the shooter, then the story jumps back to you playing as this mobster up until the same point where your boss gets shot and you give chase, but are unable to keep up, at which point we jump back to play as this guy, the shooter, who is a mercenary, a gun for hire, you play through his story, until the same point, and you find out who arranged for you to kill the mob boss, turns out it was someone trying to frame the first guy.
So now you have a choice, continue as the first guy who is trying to evade the mob as they think he is involved, while finding out who set you up, play as the mob guy who wants both these guys dead, or as the mercenary, who needs to flee the mob.
Obviously this is just something I came up with in 5 mins, it would be a much deeper, richer storyline, but it means you choose what happens, it isn't chosen for you.
It's not like redoing the same things, they are different people in different lines of crime.