Faster than humans
It is true that the precise movement of the gear stick while shifting, plus the ability to work sensitively with the clutch pedal, are a strong argument in favour of manual transmissions; this is an invigorating cocktail for anyone who likes driving. And then there’s double clutching. It’s no longer necessary for modern cars, but when an experienced driver precisely balances the engine speed by tapping the accelerator pedal when downshifting, thus changing gears without the slightest twitch, this is the best feeling in the world for a driver.
When it comes to the actual shifting speed, however, humans have been losing out to the machine for years now. In sport mode, modern automatic transmissions offer ever quicker shifting speeds, and they can make use of effective double clutching themselves. Simply tap the lever on the steering wheel and the next gear is immediately engaged. The driver doesn’t have to deal with anything else, leaving him more time and attention to focus on the actual driving. Even proponents of manual gearboxes have to admit that, in their sportiest settings, today's high-end automatic transmissions are quicker than humans, and when they change gears more slowly, it’s only to make the ride more comfortable.