No, but if you stay at Starwoods you'll earn 2 points per dollar spent on the card, plus 500 bonus points for each of the first 11 stays (1,000 bonus points for the first stay).
And the Starwood card is free for the first year, then $30 thereafter, versus a six month fee waiver and $50+ annual fee.
Plus you get a lot more flexibility because you can transfer SPG points to 29 airlines, versus none with the AA card.
Everyone's situation is different, see what's best for you.
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