BA by far, looking at the seat (fully flat on BA, angled on EI), cabin and plane (B747 on BA, so great upper deck experience). If things are not changing by October, you would land and take off from LHR T1 (so no terminal change but only regular lounges). If you choose the EI option, you would connect somewhere in the US. On the plus side, US pre-clearance is done in Dublin on most flights to the US on EI. On the minus side, you would have a shorter transatlantic flight (which I don't like since it means a shorter night).
Assuming the Aer Lingus is direct and BA indirect via Heathrow I'd take the direct flight every day. Also on the way back with AL you will preclear immigration in Dublin making for a much more pleasant arrival at SFO.
SFO - LHR with BA arrives T5, not T1, so there would be a change of terminal.
If you got the earlier flight from SFO, it means you could then use the BA arrivals lounge before your flight to Dublin.
mickt: Gosh, TI at SFO but, yes, T5 at LHR. Sorry...Edited: 5:31 am, February 11, 2013
OP: as mickt mentioned, it would be more than recommended to use the arrival lounge at T5 if you have time (it means though entering the UK which can be long if you do not hold a e-passport) since the BA lounge at T1 would be the "UK and Ireland" one which has only limited facilities. If you decode though to remain airside, the bus ride between T1 and T5 takes 10 minutes and buses are frequent.
I would say BA is the better airline (certainly better in business class) but for the reasons stated Aer Lingus might be more convenient.
Another option is Swiss via Zurich. Again, a superior business class product.
As the EI option means changing in JFK,ORD or BOS then I would go with BA. A US domestic flight will not compare in comfort to Clubworld
Agreed, if the AL flight isn't direct might as well go BA
BA all the way even if the other flight was a non-stop which it isn't.