I love the C63 (my dad just bought a 2013 CLS63 and that's the greatest car I've ever driven). The torque in AMG's is amazing and is a monster in accelerations. His CLS63 handles extremely well actually, and only loses traction if you're gunning it at full throttle out of a corner. I bet it's a monster on the track, and it has beaten the F10 M5 on numerous tracks and I'm sure the C63 is similar.
With that said, I would NOT choose a C63 over the new Cayman simply because of how awesome the new Caymans are. I like smaller feeling cars (the C63 is fairly small but is still heavier than the Porsche) that have handling like they're on rails. The C63 is definitely more practical as a DD and can handle three more people than the Porsche if that's important to you. I think the AMG does 0-60 in four seconds flat whereas the Cayman does it in 4.5, but unless it's the Turbo, Porsche doesn't care too much about 0-60 whereas AMG does. You can't go wrong with either one so it's a matter of preference. Have you test driven any of these cars yet?