Played the JG 2012 4003 today. Nice bass. Well made as usual, nothing really new about it. The neck appears to be the same width as the previous years, didn't detect anything different here. They seemed to have taken the crown off of the back of the neck's profile. There's about a 3/4" wide flat spot down the middle of the neck, making it a a little thinner in the center, but the sides appear to be the old profile. It didn't make the neck feel any better in my hand than ones I've owned before. So, the change is minimal. I think it would have been better if they had also tapered the rest of the back of the neck on the edges too. That would have been substantially new and made for an easier playing neck. Final verdict: not much better and not enough change for me to buy it. Still a nice bass though if you like the neck profile.
I did pick up a new oversized LP cherry burst and found the neck has changed on those. Really nice, narrower and a bit thinner. So, I bought it! Fits perfectly in my hands.