We have played it once, and it went quite well. Unfortunately, we're still "stuck" (though in an ejoyable way) with several D&D campaigns, so we're not actively playing Shadowrun.
What I liked:
[i[The improved dice resolution mechanic. [/i]
The new system plainly doesn't fail down in extreme situations. It has a lot more consequences then one might expect in the beginning - suddenly you're character isn't effectively disabled just because he has taken some stun and lethal damage. Smartguns are suddenly just nice to have, not the requirement to be a decent shooter. (Which means a lot for Ki Adepts).
Loss of pools
Characters can now attempt to dodge every attack, meaning that people without combat pool remaining are not automatically hit and killed by any decent shadowrunner or guard (whichever side you're on)
Skill Groups
Finally, a sensible approach to an old problem. In SR 2, characters learned "Firearms" and were capable of using all weapons. In SR 3, characters had to decide for a single weapon group (Rifles, Pistols, Shotguns and so on). Now you can create a firearms specialist and the guy only caring for his pistol, without making one of the two archetypes to expensive.
Cleaning up the magic system
Yes, I liked the old distinction between shamanistic and hermetic magic. But a lot more I love a sensibly stream-lined game system. Let's face it, the additional rules Magic in the Shadows already did blur the lines between shamans and hermeticians anyway, and the new solution makes this in a open way. I am still in favour of keeping most characters in the old reigns, but the new mechanics are fine with me.
New Hacking rules
Oh, I will probably miss the term decker, but integrating the flow of the Matrix combat into the regular combat - great idea. Now we just have to get rid of the astral space (but that was never as bad as Matrix, because at least the combat resolution mechanic stayed similar)
But there is also one glaring error in the rule system:
Initiative
Multiple actions per round simply doesn't work. It sucked in SR2, where slower characters didn't get to act before the extra actions from the others were resolved , and it sucked in SR 3, because slow characters still had to wait eternities till the cybered-up where done.
Multiple Initiative passes simply create to much imbalances.
My "hotfix": Instead of getting extra passes, people get extra (automatic) hits on their Initiative/Reaction checks. The second step would be reducing the cost of Reflex Boosting cyberware, powers and spells. Maybe 1 point of Essence/Power Point per pass/hit)
Still powerful, but not as extreme as before.