It will depend upon the route. For example, if you are referring to an ordinary domestic route such as ORD-PHX or DFW-BOS, etc. then, from my experience, I will say that AA's First Class service is better than any I have flown in the past couple of years (includes AA, DL, UA, US).
Now if you examine specific longer haul routes, for example ORD-SFO or ORD-LAX, both AA and UA fly three-class "international" aircraft on certain flights. UA sells a Business Class product in these markets while AA does not. While AA's seats on such aircraft will be of the international "sleeper" style (as UA's should be), my guess is that UA's service on these select routes may be better than AA's since they are actually selling two "premium" classes on such flights. AA's First Class on these flights probably mirrors UA's Business Class, where offered, on the same routes.
Transcon flights are an altogether different situation, and I have not flown them in 20 years, so I will leave that subject for others' comments. I suspect, however, that if CO operates any transcon flights their "BusinessFirst" product will blow most any other carrier's service away.