There are also Delta (via Atlanta or JFK), Continental (via Newark), US Airways (via Philadelphia) and American Airlines (via Chicago). Of course there are several options by the main European airlines as well but that means you have to travel 1-2 hours the wrong direction first.
It all depends what would suit you better. I have gone to the West Coast USA in both ways in the past (to LAX via Heathrow & Las Vegas via JFK) and to be honest I got there quicker by the Heathrow route; the problem is that you have to allow plenty of time in the connecting airport in the USA as you have to clear customs at the first airport not at your final destination. Yes I know that if you fly to USA directly from Dublin, you (in most cases) clear immigration before boarding the plane but you really have to allow a good 90 minutes after your clear checkin/security as the queues can be enormous.
Also, it depends if you would prefer two 6-7 hour flights or one short flight followed by a 11 hour flight. Personally I would rather to have one real long flight but as I have done a lot of flights over 10 hours, it is easy for me to say that. If you are not accustomed to such long flights you may be better breaking it up. Also worth noting that you will get food/drinks the whole way across the Atlantic with an European airline but with any internal USA flights you will have to pay for it; also you are more likely to have the small seatback tv screens on the European airlines (makes a helluva difference on a long flight)
Ultimately, it will probably come down to price, as LAX is serviced by so many airlines, you could get a return flight for as little as €450.