Hey Waverunner. I've fired the Glock 20 10mm a couple times and although I like the power (the guy was firing full power 10mm) the gun was a little wide for my hands. The same goes for the Glock 21, which I've tried too. If you've fired a Glock 21 before, the Glock 20 is physically identical but noticeably more powerful. The 10mm is more powerful than a full power .357 Magnum, is on par with the .41 Magnum, and is quite impressive. The 10mm is an excellent cartridge but with so few quality platforms, I'm afraid it is dying.
I myself carry a 3rd Gen Glock 32 .357 Sig with Meps. I LOVE this Glock. It is very comfortable (I assume you carry an NYPD G19?) and packs a wicked punch. You KNOW you're not firing a 9mm when you pull that trigger. It is quite accurate and manageable for a small pistol firing a 525+ lb-ft round. Plus, I have a factory G23 barrel that swaps out in 5 seconds to allow me to fire .40 S&W. In my experience, the hotter .357 rounds kick a little harder than the hottest .40 S&W rounds, a testament to the .357 Sig's power.
The major selling point IMHO of the .357 Glock over the 10mm Glock is the availability and quality of ammo. More and more LE agencies are adopting various .357 Sig weapons each year so this can only help with ammo availability.
G20 pre-ban mags are more scarce than G22 mags, consequently they are also more expensive. I use FML pre-ban G23 mags in my G32 and I've had 100% reliability with all ammo fired, so I'd imaging G22 mags work similarly well in a G31. So, the mag issue adds more weight to the .357's edge, hence I'd vote for the Glock 31.
Too bad you don't live a little closer to Albany or I'd offer to let you try a few boxes of .357 in my Glock 32 to help you decide. I really think you'd like the .357 Sig.
Well, good luck with your decision and hope this helped some.