PD engine delivering torque in buckets straight away while CR engine runs through revs smoother as well as being quiter
Hmm yes, broadly, but not quite in the case of later (I think) 2.0 TDIs. The advantage of PD is the extremely high injection pressures, higher than CR even, but the disadvantage is not being able to vary the injection timing because the injection event is driven from the crankshaft. So older PDs (which is most of them) do give a huge torque surge at 2-3krpm.
However, the later 2.0s also have electronic piezo control of the injection event, so the ECU has more control over the timing. This means that you don't get all the torque in one go any more - it builds up more like a CR engine. SOME versions of the electronic injectors (made by Siemens I think) are the ones that would randomly stop working, which is why you hear about dodgy injectors. However they issued a recall for it, which meant my car had a new set of injectors for free at 80k miles, which was nice.
But yeah, 2008 on is best - the PD engine is a bit noisy at lower speeds (although quiet cruising) whereas the CR is nicer at all speeds.