Love the handling comments...
I concede my M3 was more nimble at the edge than the C63C at the track and the C63 has skinny tires relative to its torque and weight; however, I think I am faster in the C63. Mine is the 2012 with the MCT, suspension tweaks and P31 + LSD. You can also look at ring times for what they are worth, the 2012 C63C PP is 4 secs faster than a E92 M3.
That being said, the M3 is a great all around car and very balanced. This guy (if the OP is not trolling) simply baited you with a faster car, there is no question the C63 PP will devastate a stock M3 coupe in a straight line, let alone a convertible. My stock C63C PP feels noticeably faster (torque partially) than my tuned, intake and full-exhaust E92 M3.
Current: 2012 C63 AMG PP | 2012 F25 X3
Past: 2008 E92 M3 | 2009 E90 335i | 2007 Z4MC | 2002 GTI 1.8T | 2000 Celica GT-S | 1999 328i | 1990 Corrado G60