As I understand it, the problem is that the PD engine can't be tweaked far enough to meet upcoming emissions requirements in the future.
In order to meet ever more stringent emissions rules, engine designers are having to do more exotic things, like injecting fuel into the exhaust stroke (don't ask me how that helps, but apparently it does).
But with PD, the injection pressure is only available while that plunger is pressing down inside the PD injector. That means it's only available at certain crank angles, because the PD injector is cam driven. So with PD you can only ever inject fuel near top-dead-centre between the compression and power stroke.
Common Rail maintains its pressure all the time, so the injectors can squirt fuel into the cylinders any time they like. It's a much more flexible system in that sense.
Very interesting post

Makes sense when you put it like that.