Priority baggage drop - by CC or MCE?
 

I know the credit cards come with free checked bags, and that MCE comes with priority boarding. But do either come with priority bag-drop?

No, neither come with priority baggage handling.

Although even though it is a Plat. level benefit, I quite often get it when I use priority check in as a Gold. My upgrade rate has been decent this year though, so some of that might have been because I was travelling in first.

If priority baggage handling is what you mean by "priority bag drop" - it's hardly a benefit worth thinking about.

IME "priority" tagged bags actually get priority handling (i.e. first off the claim belt) on AA no better than 50% of the time. Seems like they come off last as often as they come off first

I am referring merely the ability to use the Priority check-in queues at the airport. I don't care if it has the tag, I just have seen some crazy lines at PHX that I was glad to walk past, especially at the holidays.

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The Citi AAdvantage Executive World MC comes with Priority Check- In (use of Business class lanes), Priority Security (where available) and Priority Boarding.... in addition to the free checked bag.

Thanks Jagger. I might be able to do a mileage run for < $495 to keep gold, but on the flip side I'd have the lounge and free bags this way too! (If I was checking a bag sans-status it was getting reimbursed with Amex travel credit).