I just got both this week but here is my opinion and view point. I do a lot of travel for work. I got the Platinum due to the lounge access and conciegre. I got the CSP because of the points. I'm going to put all daily/living expenses on the AMEX (i.e. rent, groceries, etc) because thats the bulk of my purchases. I put ALL travel on the CSP for the rewards points. The platinum is beneficial if you actually spend a lot of time traveling or are planning to. The CSP will be much more beneficial if you plan on taking a few trips a year and will use the points to for tickets and things like that. Just my opinion though. Its whichever you plan to do.
ETA: It also depends on the airlines you have access to. I live in an area where United/Southwest is the easiest to get so the CSP is great for that. I use to live in Atlanta so I had Delta easily. My first skymiles account was with Delta. I rarely use them now unless I'm going international. Look at the partner airlines with each card and see who you would use more