I have the P380. The barrel and the engraving are the only differences. If I didn't want to spend the extra dollars for bragging rights and for features that don't add to the performance of the Pistol, then buy the CW380. I will work just fine. I have a sickness that makes it hard for me to be frugal when I need to be. My wife is gone so I have only me to care for. My buys love the toys I have and that will be theirs some day. I say, if you don't have anyone else to think about as you make your final decision, then by all means get the P380. If you are going to get yelled at (a lot) then get the CW380.
Or, buy a darn Glock where you don't have those decisions. :>) (I can't believe those words came out of my fingers)
I bought a CW. While it was at Kahr getting its striker replaced, I bought the P380 (just 'needed' it). Now, I carry the CW and use the P380 at the range and to dry fire with. The P380 'looks' good but then again there is something to say for the sharp lines of the CW's slide. I'll switch out and carry the P380 for a while but eventually one should go. Thinking about a shield.