Lately, well, ever since I've been playing at the arcades, (mind you, I play
fighting games almost exclusively at arcades, unless it's a round of
Jambo! Safari! or
Silent Scope) I can't remember anybody who didn't just totally suck using the
palm over the ball joystick grip. I used the
whole fist joystick grip as a little kid, because that's what I had to work with, then around 14, I used the overhand grip, like your standard
arcade gamers. But... when I was around 16, I think, a
change was in order for my
arcade survival.
You'll notice that the over hand grip you mention has you holding the joystick in your hand, palm down. This prevents mobility, all motion requires the use of the wrist, and sometimes even the arm. A quick hadoken, shoryuken - what have you - becomes increased in difficulty significantly when holding the stick in this position. The only real benefit I know of to this position is that it squares your shoulders so that you take up more space at the arcade cabinet. If you're already a big guy, you can force other people to play standing in odd positions. Just a few days ago I lost a couple matches to a guy who must've been 6'3" and 260 or so, because I was standing to one side of the cabinet, with my left hand barely on the controller.
Now, the underhand grip is superior, or at least, I think it is. I hold the controller with my palm turned slightly up and to my right, my index and middle fingers curled around the front of the stick, and my ring and pinky fingers behind. The thumb curls over the top of the joystick. With my hand like this, I can react quickly through the manipulation of the stick by my fingers, and I can easily encircle the stick with my thumb and index finger if I want to do charge moves or technical specials that require me to make precise movements (I usually use my arm here). Trust me, this grip makes your brain-to-stick reaction time faster, and every damn moment counts when your life bar is on the line.
As for why Asian gamers do this, I don't know, but the reason I started was because of Asian kids in arcades that would romp me viciously. I took it as a sign that either they were better than me, or they knew something I didn't, or both. I ended up getting schooled (and learning a lot) by them, and I'm now one of the higher ups at the local Penny Arcade on Royal Street.