There are really 3 shooting techniques with a shotgun: snap shooting, sustained lead and pass through. I find myself snap shooting on game but rarely do this with clay pigeons. Rather I use sustained lead on some shots and pass through on others, especially on incoming targets but primarily I shoot a pass through method on most flying objects. What technique do you use, think is the best, and why? PS: I think this question pertains to double guns and is not OT because I use these methods with these guns too. [spoiler][/spoiler]
IMO, there is another method. Don't know that it has a name, but I learned it from Bill McGuire, one of the winningest American sporting clays shooters there is. Of, course, this method is useful for pre-mounted clay target shooting only, but is a method nonetheless.
Bill teaches to observe the line of flight the bird is taking, then insert the muzzle on line just ahead of where you want to break it. Lift your head off the stock, look back toward the trap and call "Pull". Watch the bird close the distance to your gun, keeping your gun still for the moment, then, as the bird approaches your gun you establish the lead with an almost unnoticeable move and shoot. It almost looks like spot shooting, but if you watch the muzzle closely you can see a very small move, more on some presentations than others. Very deadly when done right, and easy to learn.
I use this when competing, but when hunting I use everything, I guess, all according to how long I have before I see the bird and I have to shoot.
When it's working right we all can look like a pro, but when the wheels fall off, it's bad regardless of the method used.
SRH