#1
So recently I began to correct/clean up my alternate picking. I think I have changed my technique slightly since then to pick properly (from the wrist). Nothing to big, but i used to hold my pick between my index and thumb with the index bent like this.

http://www.learnguitarblog.com/images/how-to-hold-a-guitar-pick-2.jpg

Now i hold it more like this, only for alternate picking though. I can still pick the other way, but it feels much more uncomfortable now (and almost wrong). I get a small amount of fatigue in my index when playing like that as well.

http://www.investebooks.com/images/Guitar/guitar_pick.jpg

Now that would normally not be a problem I would just play the new way all the time. Except I can't seem to sweep as well with my new way of holding the pick (I can't mute nearly as well). So are one of these ways of holding it incorrect? If not should I just keep holding the pick differently for the different techniques?
#2
Just hold it the way it feels more natural and comfortable, you shouldn't be forcing yourself to hold it in any other way, especially not trying to copy the way others hold it (not saying you do).
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#3
Altho, I do not have any pics for reference, but in my opinion, all these "right" way and "wrong" way pics are just garbage...

Take note on how, for example, Kirk Hammett's form and function with his picking hand versus...say, Marty Freidman. notice how kirk picks with his wrist while Marty picks with his elbow.

Just try to focus on the form that is most comfortable to YOU. Because everybody's dexterity and flexibility differs. this is a slight difference but for musicians, this difference affects us.

I say, if it feels right, GO FOR IT!