I haven't flown AB long haul, so can only compare AA, BA and IB. Pros and cons from my perspective are listed below. For me, considering it is Y class travel, it's a toss up between BA and AA, with a slight lean towards BA.

AA
Pros:
77W between JFK-LHR
Good seats in terms of legroom (particularly MCE if you can get it with status)
Very good IFE
Cons:
Spirits are not complimentary in Y

BA
Pros:
Same Terminal connection if traveling JFK-LHR-MUC
Good Lounges at JFK and LHR
Complimentary alcohol on board
Latest IFE if you're on the B787 to EWR
Cons:
Seat comfort and legroom (unless you get an exit row)
IFE not as good as AA's 77W, particularly as most JFK-LHR flights operated by B744

IB
Pros:
Catering and complimentary alcohol
IFE on A330 is good, A340s being progressively updated
Seat pitch on A340 is OK, exit rows is great
Lounge at MAD T4S is very good
Cons:
Mainscreen IFE on A340s
Service indifferent at best
Seat pitch on the A330 is tight.

Onboard service on all carriers can be hit and miss – IMHO BA would have the edge for consistency, but I've not had any real problems with AA. As noted above, IB crews can be indifferent at best, although better if you speak Spanish.

Can't really advise on IRROPS. I've not had too many occasions where I've needed assistance, however I've always found AA staff to be helpful in adverse situations. Status helps a lot.

Hope you find yourself right at home with oneworld.