If you need someone to convince you here to get a M3, maybe it is not for you. As for C63, power is there, the jury is out on how it will handle, and looks are "ok" IMO, not a fan of the rear....looks like a Honda Accord. CLS 63 is BAD ASS, but nothing like the M, more like a 5 Series/M5. Closest car would be a 996/997, if you can find a good deal on it.
The M is a "driving" car, handles AMAZINGLY, and huge aftermarket support. If you like to "drive", care about modding/huge aftermarket support/community....Go with the M. If you do not plan to mod, not big on the aftermaket parts, just want to haul ass in style, AMG, Porsche, Audi, or any equivalent.
Good Luck in your search.