Well having worked for both carriers I think I can give an unbiased opinion.
EI only have one A330 (EI-DAA) which has personal IFE in the seat backs and even then the choice is limiting. However the seats are generally an inch or two more spacious where legroom is considered even on the Airbuses without PTV's. Also you get more in terms of food on EI than you do with BA BUT you have to pay for your booze.
BA have a pretty good IFE yet its not of the AVOD style. The seats only have 31" pitch which I personally find bone crunching (Im 6'1") but if you arrive nice and early at the desk (in LHR not whatever other airport you may be connecting from) you can try and get a bulkhead/exit row seat of which there are about 20 or 30 depending on the aircraft config! You also have a free bar throughout the flight (yet somepeople will try and tell you otherwise because these people are too shy to ask for drinks midflight as they expect the crew to do a bar round every 30 minutes!!!)
I personally would go with BA but if its a quick and direct flight I would chose EI!!!