As a DL DM and an AA EXP I have a fair amount of experience with both airlines. Value and performance are always based on what matters to you. Overall I think that DL is a far better and more consistent airline. AA is going through a horrible spell right now...to the point that is has fallen below UA in terms of service and quality. Here's my take on DL vs AA and who is better:
Website: AA
App: DL
Pre-Flight Info on delays: DL
Ticketing and Check-In Experience: Tied
Upgrade Frequency: AA
Lounges: DL
Lounge Food & Beverage: DL (though the Flagship lounges blow everything away)
Hubs: DL
Aircraft Interiors: DL (AA still has mainline aircraft with no powerports)
International Business: Depends: AA 787s are great, AA 767s are beyond lousy. DL A350's are heaven. DL 330s feel like coffins - I'll call it a tie
On-Time Reliability: DL
IRROPS Information Sharing: DL
Cancellation Rates: DL
Regional Carriers: DL
Pleasantness of Employees: DL
In-Flight Food and Beverage: Tie
Award Availability: AA
Final Score: DL: 11 AA: 3