I don't agree with saying that *all* manuals are faster than auto's.  It's not true.  Look at the acceleration times of a CVT car.  The auto is a full second to a second and a half faster than the manual.  The auto CVT also pulls better gas milage as well.
I would say that in a N/A 4 cylinder, and some of your smaller 6 cylinders, the manual will almost always be quicker.  They already have low HP and Torque ratings, and the slushboxes on the autos suck up valuable power making a greater hit performance.  Also keep into consideration that these smaller engines generally have their powerbands at higher RPM's where automatic transmissions have trouble staying at.
When you move up to big V6's and your V8's, things start to change IMHO.  The powerband moves down to the lower end of things, and much of the power is usable at low RPM's.  In these sorts of engines, they have enough power to overcome the drain by the auto tranny, and infact, are efficient enough that they can shift better than the guy with the stick.  It also helps that they have low end grunt so if the auto tranny decides to upshift on you, you can still accellerate well.  The same can't be said for a high reving 4 cyl.  
Outside of "start from a stop" acceleration, one place where manuals shine, especially in high reving 4 cyls and small sixes, is in the fact that I can keep the car in the power band myself.  I can run any gear at 6,000 RPM's and keep it there provided I have the road to run it.  When I go to pass, I can take it out of the overdrive gear, drop it into third, and then rocket past the other car.  Can't really say the same for auto's.  The auto tranny will take a second to register I am trying to accellerate, and then it will many times put me outside of the powerband on the initial takeover.  I don't get my power until I'm past the other car.  With a manual tranny I get my power when I want my power.