The AmEx Platinum is a hugely popular credit card. The biggest overcrowding in lounges I've seen are: Centurion, Sky Club, Priority Pass lounges. All are accessible if you have the AmEx Plat.

AAdmirals Clubs are, with a few exceptions, not crowded.

Note that the changes Delta is making do not lower the benefits for AmEx cardholders, only for Delta members. We talk here about how AA is a credit card company that flies planes on the side. Seems like Delta is similar.