I, like many golfers, used to have a strong and slowly migrated to a neutral one. Along the way, I found out a couple of rarely mentioned facts which have firmly convinced me that a neutral grip is generally superior to a stronger one. Not that you can't hit great shots with a strong grip, but those with a weaker grip will still have certain advantages.
There are the well known benefits, such as being able to work the ball more easily and the ability to hit higher shots. A couple of benefits, however, seem to have flown mostly under the radar.
A weaker grip allows you to more easily set up with your forearms and shoulders on the proper plane, so you can turn on the proper plane. A stronger grip requires some more contortion to get thing aligned.
In addition, it allows you to more easily set the clubface open at address- a technique both Ben Hogan and Jack Nicklaus used. The purpose, however, is not necessarily to promote fade. Since the clubface is rotating throughout its arc, a clubhead set BEHIND the ball should be open, in order to allow it to square up as it closes traveling through the ball. This is important to actually align the face correctly, but also because it gives you a clear visual cue that you can fire through the ball without shutting down the face. For many players, a square face at address will make them feel as if they have to "hold" the face square through impact, instead of allowing it to release through.
Finally, possible the most important reason. A sufficiently weak right hand grip (which some combined with a stronger left, a la David Duval) will allow you, in concert with a proper turn back, to set the club on the pad at the base of your right index finger when you reach the top of the backswing- otherwise known as pressure point #3, in TGM lingo.
Richie3jack's blog has some good diagrams of PP#3, as well as a lot of good info on TGM.
So, why is this pressure point so important to set at the top? Because this is where you apply the power! By putting the club in a position that loads up this point, you can start applying power through the ball from the very top of the swing.
This was the beauty of Mr. Hogan's swing. By setting the club on the same plane it would travel through the hitting area at the top of the backswing, and setting its weight squarely on top of the most powerful part of his right hand, he can simply hit as hard through the ball. The face will rotate naturally through the application of power through this point without manipulation, and sufficiently weak grip will also allow you to hit freely without worrying about a hook.