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I think the biggest contributing factor should be type of driving you will be doing. Mine is purely for pleasure driving and I love the manual 6 sp.
Between Camaros, Firebirds, and vettes I've had five six speeds and loved every one.
But my daily driver is a Silverado w/auto. I get stuck in stop an go commute traffic many times a week and a stick gets to be a pain in **** in heavy bumper to bumper stop and go. Also, are other people going to drive it? I wouldn't trust anybody with my clutch, too tempting to matt the gas and dump the clutch.
But for the flat out which is quicker question. Generally a stick is quicker, due to a slight power loss in the auto's convertor.
Can't go wrong with either, will really just be a matter of preference and driving style. Daily driver and other family members going to be driving, I'd lean toward the auto. Pure weekend pleasure and you've enjoyed stick shifts all your life - M6.
IF you can drive a manual the way it should be, it will be faster than the A6. (but not by much)
But give the aftermarket a bit of time to develop a high stall converter, modify the shift points, and defeat part of the torque management (not all of it or that 2.xx rear will shuck right out of the car), then the auto should win nearly every time, even against a good manual driver. An auto shifts quicker and more consistently than any human can.