ive come from a DSG gearbox and ive also driven a PDK and the first difference is that the 370z is not a dual clutch system like the DSG/DCT/PDK
shifts are fast but not instant, they are jerky and you can feel the shift. this is more noticeable in manual mode (paddles) and also higher up in the rev range.
downshifts are nice, you get the same rev-matching as the DSG
ive driven other non-dual clutch autos, e.g. in the Mercedes c63 and also the non-DCT BMWs and also non-DSG Audi and I would say the 370z has one of the best non-dual clutch gearboxes.
there is no 'lag' between hitting a paddle and shifting. and you can actually downshift 2 or more gears faster than a DSG would.
in short, its very good (better than the c63) but not as good as a dual-clutch (which is only available on the GTR)