NRA Shotgun training manual:
Five Fundamentals of Shotgun Shooting:
1) Stance
2) Gun Ready Position
3) Swing
to Target
4) Trigger Pull
5) Follow Through
Follow the target with your shotgun, when you get to it, fire, while keeping your bead following the targets trajectory, even after you fire. If it's a clay, follow a piece to the ground, if it's a gamebird, follow the bird to the ground.
"Follow through takes care of what is often refferred to as the lead. In the swing through method, measuring (or guessing) lead is not necessary because it is automatically taken care of when the shooting method is executed properly."
It worked for the kids I teach at summer camp, (had two boys score a 196 and a 197 out of 250 after showing them how to shoot) on a trap setup. It works well for hunting as well. I always outshoot the guys who try to lead their birds
If leading works for you, go for it. If the follow through method works, use it. If you're only shooting one type of sport, such as trap, or skeet, then it boils down to what's comfortable for you. If you're shooting in different venues, like sporting clays/trap/skeet, or hunting, then the follow through method will probably work better with the different speeds and trajectories of targets.
Just my $0.02