I was self-taught, so have always held the pick in the "wrong" way: between tips of thumb, index and middle, something like holding a pen.
Mostly it's between thumb and middle, with index supporting the front edge (touching the top curve).
I have occasionally tried the "correct" way. It feels very clumsy and awkward to me, which is of course because I'm so used to my way. I have noticed, however, that scale and lead playing can be faster using that grip, because the hand movement is more minimal. The problem is I find it much more awkward strumming with that grip, because my knuckles seem dangerously close to the strings.
Also, the "correct" grip doesn't give me as much control over pick angle or attack as mine does. My 3-finger grip allows a lot of flexibility of angle and pressure. (Of course that's not why I chose it: I just held it how it felt most natural.)
So I know my grip has a downside (no shredding for me
), but I also feel the recommended one is too fixed. (But I'd accept that's only because I've never sat down and properly practised with it for long enough.)
I'm also encouraged by the fact this guy holds it the same way I do (most of the time if not always):
(Pat Metheny)
If you want to get real anal about it, the most comprehensive essay I've seen on pick technique is this:
http://www.tuckandpatti.com/pick-finger_tech.html
He recommends George Benson's variation, which is something like Metheny's - and also close to the one I arrived at intuively, 47 years ago. (Unfortunately it doesn't make me play like Metheny or Benson
.)