First up, in Britain we call it Gear Acquisition Syndrome but it's something that many musicians suffer from. Lots of people spend lots of Euros and Pounds on great amps by Engl (amp of choice for another master alternate picking guy who, hint, also flies planes), Mesa (Petrucci), Victory (Rob Chapman, Guthrie Govan), and Koch (Al Di Meola). Guitars. Yup, we like guitars. And don't get me started on pedals (think I had five different compressors at some point).
But the fingers and the pick by extension is where it's at. Van Halen always sounds like Van Halen, come what my.
Physics bit: with Jazz III style picks, more power is transferred to the string because there's a greater transference of energy from your fingers to the nickel and steel.
This doesn't result in a tougher tone, just the less kinetic energy is wasted. More about that in a minute.
There are two kinds of Petrucci picks, I think. These are the more expensive ones, but they are so worth it. They're exact copies of the very picks the man uses. They are very easy to grip because they are like those old Rhino type picks they sold back in the nineties. They will not fall out of your hand. Which is just as well because if you lost one on a dark stage, you'd never see it again.
When I said less kinetic energy is wasted, I didn't mean this makes things easier. In fact Jazz IIIs need more precision, just like Petrucci. You've got to practice (or you could always buy some Paul Gilbert picks, which always make me sound better than I really am). My own set-up is Jazz III, Kotzen Telecaster, TC Flashback, and sometimes some Fulltone stuff, into a totally unforgiving THD Bivalve. If I screw up, and sometimes I do, it's like I've got a "kick me" T-shirt on. But if I'm up to speed, ain't nothing like making things hard for yourself (pardon me vicar).
If you're up to it, give these a go. The challenge is a learning experience and the results are awesome.