I have always found Aerolineas the cheapest, you have to go via Madrid and there are always delays, but if you go purely on price I suspect they will be your best bet
Christmas 2007 I travelled with American Airlines via Chicargo one way and New York the other as at the time this was the cheapest. You have to put up with rude and arrogant immigration in the States and there is anything up to twelve hours between flights. Two long hauls? not for me I'm afraid.
I think the best bet is one of the national carriers, Air France (my favourite) KLM (via Sau Paulo and Amsterdam) Iberia or Al Italia or Lufthanser are all competitive.
The trouble is in July that is the school holidays here and for some reason that bumps up the prices to Argentina.( avoide Summer and Christmas travelling)
British Airways , who as far as I know are the only direct fight, I have always found to be almost twice the price of the others.
Theses are my experiences, if you find anything better, please pass it on (I travel usually twice a year).
TAM and Iberia are generally your best bet from the UK. BA always are expensive and unecessarily slow. Immigration in the US is a bitch. If you fly from Dublin you do US immigration in Dublin airport and are very nice.
Im trying out Iberia for the first time when I return in June. I have heard bad reviews about them. I chose them because I wanted an excuse to fly from the new T$ in Barajas! I will get a sleeping pill and knock myself out for the whole flight!