If you are going to use the cards for any material amount of spending, consider whether you would rather get AAdvantage points or Membership Rewards.

You might also review the actual lounge policies for the AA card vs. Amex. Sometimes there can be subtle differences, for example, number of guests.

Amex Plat also provides a few other perks, like elite membership for Hertz and (I think) National car rentals.

Note any signup bonuses. Sometimes the airline club-inclusive cards will come with a reduced first-year fee but no signup bonus, while Amex Plat will give you a signup bonus (shop around different links for the best one) but the $450 annual fee is inviolate - but you're not paying it.

Finally, you are probably elite on AA and getting most of their perks, but the $200 fee rebate on Amex could be useful to you on other airlines when you have to travel on them.