The cars put out very similar wheel horsepower figures in stock form as the C63 AMG Black Series shows ~430 wheel horsepower on a Dynojet. With a tune this can approach the 460 wheel horsepower range depending on how aggressive the timing is and the fuel quality. The stock torque figure is roughly ~405 lb-ft of torque at the wheels whereas the S55 in the M3/M4 shows 429 lb-ft of wheel torque stock.
Once tuned, even with a modest tune, the M4 exceeds the C63 Black Series. Horsepower rises to over 479 at the wheels and torque at the wheels goes to 484 lb-ft. Combine the power and torque advantage with a quicker shifting dual clutch transmission and the M4's roughly 400 pound lighter curb weight and you get the result you see here. Not to mention the C63 AMG Black Series aerodynamics also create more drag.
The M4 continues to pull impressively to 175 miles per hour and the C63 AMG Black Series is too far back to even be seen. AMG fans will no doubt be quick to point out that if you boost the C63 AMG Black Series things change in the other direction.