My wife drives a 987 Cayman S and I drive the M3. I have not yet driven the 981 Cayman but I do have some opinions based on the previous version.... I think the Cayman is a fantastic car. The handling is sublime and it is plenty quick. I had test driven many Cayman's in the past and always felt like they were out of breath. Porsche made significant improvements when they went to the FSI engine in 2009. I would not consider a Cayman with the earlier engine. I have not modified the Cayman to suite my tastes so it's a little difficult to compare my modified M3 to the stock Cayman but...
There are a few things that make the M3 more appealing for me.
1 - Engine note (especially with Akrapovic Exhaust),
2 - More room in front and rear (I drive with the front seats all the way back in the Cayman and I'm only 5'11"),
3 - DCT transmission is much smoother than PDK
4 - Better electronic interface (say what you want about idrive; it's still much better than the Cayman's glorified radio).
1 - I love the full leather available with Porsche (dash, doors, center console, etc.) - I would not buy a Cayman without it
2 - Neutral handling
3 - Sports car styling
The 981 improves upon all of the advantages of the 987 plus it offers interior electronics that better compete with the M3 and styling that is much more aggressive / masculine.
'04 E46 M3 - Jet Black - Sold
'08 E90 M3 - Alpine White - Sold
'13 E92 M3 - Silverstone II - Sold
'13 E92 M3 - Alpine White - Ohlins TTX, AP Racing BBK, Cobra Seats, Akrapovic GT4, BBS E88, Volk TE37, OE GTS - Aero, 1/2 Cage & Seat Delete