Just wondering what you guys think is the better technique, and why. When I play fast, I use economy picking, but my guitar teacher wants me to try to start using alternate picking more. He says that it will lead to faster playing. Any thoughts?

what is economy picking?

Basically it's like alternate picking, except for one difference. Say you are ascending the G major scale (three notes per string pattern)... if you are using alternate picking, when you play the third fret on the fifth string, you would be picking in an upwards motion right? Well in economy picking, you would use a downward stroke, so in effect you are kind of sweeping from the sixth string to the fifth string. Get it? It's kind of tough to explain, but a simple enough concept. To me, it comes more naturally, and you can get some good speed with it. However it doesn't always work out that you are able to make two downward strokes in a row, and also it can sound a bit unclean unless you're carefull.

Imho alternate picking is safer. While there are people who totally burn with economy picking (jimmy bruno comes to mind,) its easier to have a steadier, cleaner, tighter sound with alternate picking. Economy picking takes much more practice to get really smooth and clean, and what little you gain in speed is probably not worth it. There are people who play great both ways though, and its really preference.
Some say elbow picking is better, some do fine with wrist picking (Al Dimeola, for one.) Some say the picking motion should come from the thumb and forefinger.
I think that technique is a very subjective thing for guitarrists, there is no one right way to learn. Do whatever is comfortable for you, however, if you can't get economy picking to sound clean, and if your time isn't what it should be, then consider practicing alternate picking.

Which way is better? There is no one right way. You should learn as many different forms of picking as you can and then integrate them. My entire style was developed as an attempt to get away from (a) the one best way and (b) the tendency to alternate between techniques. The trick is to synthesize techniques, in this case, picking techniques.

You should head on over to my site and download a couple of my "tunes" to hear what I'm talking about. It's not a little bit of alternate picking and then a little bit of sweeping, etc....it is one wholistic appraoch that fuses all forms of picking into one form all simultaneously -- including hybrid and circle, alternate, sweeping, and tapping! The results are quite horrifying to ears raised on Satriani, Vai, Yngwie, et al...in fact, most people who connect with my "music" are people who appreciate the frenzy and wreckless abandon of Vernon Reid, Buckethead, Reeves Gabrels, etc.
http://shredlikehell.com

Reading bofatron's post, I realize that it also has to do largely with what kind of music you want to play. I am basically a jazz player, so I focus more on improvisation, voice leading, comping style, chord melody playing, the point is that pick speed is not the focus, it's just something I practice so that when I solo I have the necessary technique. If you are into shred like bofatron, where the focus is the technique, then his advice is right. Learn lots of different picking techniques and left hand legato techniques and such, because there are so many people out there who can pick harmonic minor scales really fast, its not something that can make you even remotley unique. In my opinion, technique is not something that can set you apart from the crowd in any meaningful way, but I guess if you're going to try (that would seem to be the goal of most shred players) then bofatron's advice is the best to take.

Cool, all good advice. Thanks guys. bofatron, I tried downloading one of your songs and it wouldn't work. Let me know when that i-drive thing is cleared up, I'm looking forward to hearing your stuff.