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+1 to the poster above somewhere. I was denied for the CSP two years ago but was approved for the Amex Plat on the same day. Charge cards are much easier to get because you have to pay them in full and so the credit requirements aren't as harsh as a Revolver.
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