According to this Blog post by LensRentals.com owner Roger Cicala, the 5DIII has less than 1/2 the standard deviation of the 5DII with regards to Phase detection Auto Focus. But to get that additional benefit, one must also use Canon lenses introduced since about 2010. All of the testing was done using the center focus point.
In general, using the center focus point should yield faster, more accurate focus with faster lenses such as the 50mm f/1.2L and f/1.4. The 5DII can be an exception to this rule. When shooting in AI Servo AF, if C.Fn III-07 is enabled, there are six small AF Assist Points clustered within the spot metering circle that are active in addition to the Center Focus Point. The location of these six AF Assist Points are not indicated in the viewfinder! Yet the camera may be using one of them pointed at something that has higher contrast than what is located behind the square in the middle of the viewfinder when it decides the focus distance.
Here’s the Map for the 5DII’s focus system.
The entire series will tell you just about everything you’ve ever wanted to know about phase detection AF accuracy and consistency.
Autofocus Reality Part 1: Center-Point, Single-Shot Accuracy
Autofocus Reality Part II: One vs. Two, Old vs. New
Autofocus Reality Part 3a: Canon Lenses
Autofocus Reality Part 3b: Canon Cameras
Autofocus Reality Part 4: Nikon Full Frame