Which method of shooting clay targets is best?

You need to have all three in your skill-set when step onto a clays course. When shooting Sporting Clays it is all about the target and depending on the target presentation you want to be capable of matching the method to the target. Swing thru, pull away and sustained lead are the big three methods establishing forward allowance. Recently the 'intercept method' or 'bump method' has been in the shooting magazines. This appears to be form of diminishing sustained lead which may be useful as a last resort on a target that got the best of you on release. IMHO, its usefulness is questionable as a routine approach to a large variety of targets. Given all of the above, most competition S/C shooters have one or two 'bread and butter' methods and the use of all methods if the need arises. Skeet usually rely on maintained lead and swing thru and most trap shooters seem to use swing thru.

There is also the point or snap shot which only has limited applications for clay birds but it does have it's place.  A target which can only be viewed for a very short period of time or the second bird in a pair that is viewed only briefly as it disappears could be canadates for a snap shoot.  I use this method more on grouse but it has helped me on the clays course.

I agree with Ken.  I do use maintained lead more, but all versions will be needed on a compeitive course.  Clays is a GAME and to be good at the GAME you should learn all the moves....so to speak.