I am a long time San Diego based Delta Diamond Medallion and a newly minted AA Executive Platinum, as well as a Companion Pass holder on Southwest (yes, I fly way too much, mostly in coach internationally). I figured I can give some insight as to the differences between AA and DL Status (WN is a different product that only has mileage accumulation as a data point.)

Mileage Accrual (WN>AA>>>>>DL) Southwest wins for accrual rate for me as my fares tend to be last minute non-stop flights. On their Business select fares, I accrue a lot of miles, and reward redemption is easy and transparent. Big downside is limited redemption options.

As I fly mostly coach, AA mileage accrual is head and tails above DL. I'll often earn 3-4 times as many miles on AA. As a San Diego based traveler, most of my AA/DL flights are long haul and tend to be relatively inexpensive on a cost per mile basis. I realize AA will eventually change this as DL and UA haven't lost many flyers (well, DL did lose me for half my miles as I never would have sampled AA if they hadn't made the change), but I'll enjoy it while I can.

Operations (DL wins) DL hands down over AA. Everything from on-time to IRROPS flow smoothly on DL. On AA, flights seem to be late more often and IRROPS cause major issues which aren't quickly addressed even for Executive Platinum.

Domestic First Class (AA wins) Edge to AA. Significantly better meals and better service in the front cabin. Seats are generally bigger, but fewer planes have in seat video. The video doesn't matter much to me as I've seen it all after the first week of the month anyway, but may be more important to other flyers. Upgrades also seem easier on AA once you are EXP vs. DL Diamond.

Tier Benefits (DL wins) 8 global upgrades one way vs. 4 on DL. Upgrade certificates seem equally usable. But DL gives you 3 swipes and options for tier benefits (platinum choice and diamond choices). Overall, I have to give DL the edge.

Day of Flight Items (AA wins) Same day confirmed still exists at AA and isn't harshly restricted. DL gutted their same day confirmed options and it makes a huge difference for me. I really miss the DL flexibility in the old days. If I have a flight where I may want to use this, I always chose AA.

SkyClub vs. Admirals Club (AA wins) It's amazing how little I use these on domestic itineraries since pre-check started. Unless you drink heavily, the AA clubs I've been to are much nicer and much less crowded. AA First Class lounges on Intl itineraries are great as compared to DL options. However, you do not get free lounge access on AA unless you are flying international, where DL gets a free membership. AA partner lounges are about the same as DL. (VS at LHR still my favorite, but QR at DOH is a close second.)

Intl First Class (DL wins) A toss-up for lie flat bed flights, but on AA you need to be careful to make sure you get one. DL has them pretty much fleet wide.

Oneworld vs SkyTeam (AA wins) No contest here. Qatar, Cathay, Japan vs. AF,VS, Korean, and KLM. The lack of lie-flat seats on KLM and AF is frustrating, and the lack of connecting options on VS are highly frustrating although I love flying VS. Qatar is such a huge plus. Business Class on them is truly heavenly.

My two cents. Ready to have the community fire away at my opinions.