So, to the seven-legged elephant in the cockpit: the manual transmission. Based on the PDK's fundamentals, the seven-speed manual has a slightly shorter ratio for third and a longer seventh, but it's otherwise almost identical. At first, it's weird driving a car with so many gates, but once you find a nice, rhythmic section of road, you realize it drives just like any other six-speed 'box. The seventh gear really only comes into play on the highway.
Shift into seventh and it's clear why Porsche chose to add it: engine revs drop to near-silence, fuel economy picks up, and there's still enough torque left over to power up hills without the need for a downshift.
The PDK, on the other hand, has the same number of gears, and for anything but tight autocross-style work, it's the better choice. Lightning quick, neck-snapping gear changes in Sport Plus mode meld with silky shifts when cruising. Grab the paddles yourself for a healthy dose of engaging fun, or let it do the work for you--it's surprisingly adept at figuring out how to act based on your inputs.
In either case, one of the most notable differences from the previous 911 is the quickness with which the engine revs, on both the Carrera and the S. It makes the car easy to rev-match on your own (with the manual) and it makes the computer's rev-matching almost instantaneous.