Hmmm... I see how it leans toward UA... then again, AA 2mil status is not far off either.
But if I were someone who flew as much as the OP seems to and such a toss up were presented to me, I would base it all on service and how the company conducts itself (and not just my status). Yes, let's take this to a different level, shall we?
For example, how does UA handle the little things? The glitches, the problems all of us travelers face when flying? Considering issues found in here or with people we may know of who fly either airline, how does UA's website mishandle issues with Foreign US residents who have
green cards, for example, and sometimes cannot check in online because of annoying UAL site errors, or what their performance has been with on time flight arrivals or lost baggage, or how they handle customer complaints (with UA, one cannot SPEAK to Customer Service, one has to write to them only), and issues like that.
Compare the airlines in this way... How does AA handle all of these same things for you or people you know? Why, you could even go further and base it on how the two airlines invest as a company and whether you agree with their choices, or what political issues they support or align with that you may also like/dislike...
My opinion is that someone who flies as much as the OP is considered a highly valued customer on these airlines. At least they take notice of something when a 1k flies, right? Or at least one would think/hope for.
That being said, it is these fliers who can, above all others, make a bit of a difference on customer service issues if they decide to fly carrier A over carrier B. Thus, this is exactly where the OP can make a difference for himself and others, and said OP is therefore granted a very interesting gift.
Me in the same situation? This time I would pick it based on the one that does a better job for you or those you know.

MM
What is Delta you ask? Well, take a look at the Delta Gut: To measure your Delta Gut, suck in your belly and wrap a tape measure around and jot down the number. Now let it out and do the same. the difference = Delta... and that's your Delta Gut. 