Up to a year or two ago, I found it cheaper to book flights through ebookers etc but it seems that in a lot of cases, you will get the same price direct from the airline. Haven't booked Aer Lingus this way though.
One thing I do find great about third party websites is the ability to make multi-stop bookings and also to make bookings from Ireland (when you need to make a connecting flight) where some airline websites will only allow you to book from their European hubs e.g Thai Airways website will not allow you to book a return trip Dublin - London - Bangkok but only allow you to book London - Bangkok but a website like ebookers will allow you to book the whole through flight