This is coming from a DL flyer, so may be biased, but I've got a fair amount of experience with UA and I think I can offer some opinions. Very little experience with AA however.

Business Class:
I think Delta wins here hands down. DL's worst hard product in D1 is better than United's current best. Polaris may change that, but we'll have to see what DL plan to introduce on the A350. Soft Products are comparable, but I'm going to give the edge to Delta, from my limited personal experience in both I think DL are just slightly more polished and their FA's are a little friendlier.

Domestic First:
Much of a muchness really, though DL do have free AVOD on a much larger percentage of the domestic fleet than UA do. Service is pretty similar. Pretty much every plane on both airlines I've flown recently had Wifi.

Economy:
DL win big here, their recent upgrades have really refreshed the fleet, and the vast majority of their planes have Wifi, Power, and AVOD along with mood lighting and huge overhead bins.

Route Network:
Domestically I think the route networks are pretty comparable and it all depends where you live. I live in NYC and so have the choice of both, but I absolutely hate EWR so I tend to avoid United unless the the price is reasonable.

TATL they're pretty similar, I think DL may have a few more destinations themselves but with codeshares its much of a muchness again.

TPAC I think United has the edge, but its a small edge and DL have been expanding in the region.

South America United absolutely dominate. SkyTeam only has 1 south american member in Aerolineas and DL really only fly to the major capitals.

Reliability:
DL's on time percentage is way better than UA and AA. Anecdotal, but I've only had 1 real incident with Delta involving requiring some passengers do deboard and rescan boarding passes, which only resulted in a 15 minute delay for which DL awarded me a a ton of miles. UA i've had several incidents resulting in 30+ minute delays, and their flights frequently seem to be overbooked. Especially considering I mostly fly DL out of JFK, UA should have an advantage out of EWR, but it doesn't seem to materialize in reality.

Thats my overall impression, but as I say I'm a frequent DL flyer so I may be biased. Hope this helped! and let me know if you disagree.