Hey Deer

I have both the amex platinum and starwood. I fly a lot as well and stay at starwood hotels. I like having both cards and the flexibility to use either as and when it suits. The starwood is great because you can transfer 20,000 points into miles and get 5,000 bonus miles (ie 20,000 points gets you 25,000 miles = 1 free ticket). But the amex platinum has many interesting perks like companion ticket on domestic flights which I have found useful.

I'd get the starwood and use it with the amex.