My dad recently bought an M coupe, and we looked very hard at the Cayman S. It is, no doubt, an awesome car. Very fast, great handling, looks great coming down the road.
With that said, there was some sort of factor that neither of us could explain that kept us coming back to the M coupe. It was like the "wow" factor, I think. I anticipate that this would also be present with the M3--it was like more raw and more fun to be in the BMW at the same time. The Cayman S just didn't have that factor, for us anyway.
Either way you go--you're gonna have a great car. Good luck with the decision.
Current - 2015 981 Cayman S
Past rides: 2014 F22 M235 - MT, CWP / 2011 E82 135 - LBM, N55, DCT / 2008 E82 135 - AW, N54, MT
2007 E92 328 - JB, N52, MT, ZSP (traded in for 135)
2007 E92 328 - JB, N52, MT (retired by a drunk driver)