As a frequent user of both products, this is what I've observed:

US has:
1. Consistent PDB
2. Consistently good service in FC

US lacks:
1. Adequate lumbar support
2. Decent FC legroom
3. In-seat power

AA has:
1. Many of the things US doesn't: power, IFE, supportive seats, etc.
2. Minor detail, but I like the fold out drink tray and the little flip down tray between the seats - gives you more places to put stuff without taking out your tray table.

AA lacks:
1. Consistent PDB

As far as service, AA seems to range from average to world-class. (I had two bad F/A experiences in two years: once on Eagle ORD-CLT in Y and again on LAX-JFK in F.) When AA gets service right, it's as good as CX: smile, acknowledgement by last name, proactive drink refills, a "thank you for flying with us" followed by mints ten minutes before landing. I've not experienced this level of domestic F service on UA, US or DL, so take that for what it's worth.

Worth noting that, since I fly a lot of tcon US (and, as a LAA flyer, received few upgrades prior to this month), the service in US domestic Y is generally pretty rude and short... though I have managed to immediately turn some frowns upside down as soon as I've presented my EXP card to pay for my beverage. In Y on AA, they already see I'm EXP in the manifest, so I've always received good service.

TL;DR: US F service consistently good, hard product below average. AA F service average to superb, hard product good.