I have access to a variety of domestic airline clubs - AA, Delta, Priority Pass, Chase Sapphire/Amex Centurion, etc. People want different things out of lounges. But on an objective basis, Admirals Clubs simply offer less than SkyClubs, Centurion Lounges, Sapphire Clubs, etc. I can't compare to United Clubs as I don't recall ever entering one. Apparently the Capital One Clubs are good, however. At the end of the day, at American, the food offerings are weaker, decor is outdated, etc. Some of the clubs are more spacious and quiet, which can be good for some travelers, but as someone who has paid for access via the Citi Executive Card, and as someone who is more of an occasional AA flyer, I don't think I am getting the bang for the buck paying for Admirals Club access.

I have visited two of American's better clubs - DCA and LGA. Both are fine. However, the Admirals Club at LGA is apparently inferior to the Chase Sapphire Lounge in the same terminal. I don't know exactly where the DCA Centurion Lounge is opening, but it may provide competition for AA as well.

AA also simply suffers from a lack of clubs compared to Delta. Here are some non-hub airports where I have flown recently where AA does not have a club, but Delta (for example) does. When flying from these airports back home, particularly on business, I am not considering AA because I may want to have access to a club at these locations:
New Orleans
Kansas City
Jacksonville
West Palm Beach
Fort Lauderdale
Seattle

The bottom line is that AA's club offering is weak - and with the introduction of additional credit card clubs like the Sapphire clubs, it is difficult to justify for fee of the Citi AA Executive card if you are primarily attributing the fee to lounge access. When the new fee posts, I will likely downgrade my Citi AA Exeuctive card and re-upgrade my Chase Sapphire Preferred card to a Reserve, so I get unlimited access to the Chase lounges.