What follows is my response to another thread on the matter. The short answer is that they are technically better, but whether it's worth the price tag or the learning curve is a question best left to the player...
If you miss shots because you are shooting with english without compensating enough for squirt (a common problem) or not hitting the cue ball exactly where you intend to (even more common), shooting exactly the same way with a LD shaft will result in you making at least some of those shots. It's not magic, and it won't turn you from a D player into an A player, but it does make the game slightly easier.
It's both theoretically and experimentally proven that LD shafts reduce squirt, which reduces the possible range of squirt when applying english. Reducing the range not only puts you closer to the center ball line so less compensation is required, it also is more forgiving on cue tip placement; your tip offset can be more off target and you'll still make the ball because the deflection hasn't changed as much. It's a little like enlarging the sweet spot on a tennis racket or a golf club, you get the desired result across a broader margin of error.
If you want to have every possible equipment advantage, a LD shaft is the way to go. If you are so used to compensating for the squirt of a regular shaft that the forgiveness of a LD shaft is not worth relearning the necessary adjustments, then don't change. In particular, if you play using backhand english all the time and don't want to give that up, a LD shaft is going to cause you problems.
In either case, if you aim perfectly, compensate correctly for squirt, swerve and throw, and hit the CB exactly where you intend to, it won't matter; the OB will split the jaws of the pocket. Once you get above a certain level and do all of those things well enough (considering that there is almost always some acceptable margin of error), the game is more about position play than making balls, and a LD shaft doesn't really help you there.
