OK I'll just get started with some stuff
MATCHED
+grip for both hands is identical
=good for reversing stickings
=good for open handed playing
- ???
TRADITIONAL
+supposed better nuances and sounds than matched (but I play matched and have the same control I don't understand people that say this) mostly jazz players advocate this
+this is the only real advantage i see of this grip=easy to do crosstick without tricky manipulation of the stick...
-range of motion is decreased. In traditional grip your stick is naturally turned a little more inwards, meaning it overlaps with range from your other hand, annnd you have to turn your arm more to the left in order to reach that direction than you would with matched grip.
-you have to learn totally different grips, techniques, and work different muscles in your two arms.
() originally developed in marching snare drummers who had their drums severely tilted to one side and away from them, so as to not damage their wrists with their left hand's grip. Of course you can still tilt your drums away from you if you want, but thats just a note