At the minute there are no flights between the two cities - I am not sure but I think Aer Lingus used to operate some on the way to JFK, ut this may have been to SNN, both or neither!
In regards to the Enterprise train service - its quite disappointing. Its only 100 miles between the two cities, it takes two hours, is often late, and the trains themselves, while a huge improvement on both regular trains on both sides of the border (they are similar to Eurostar carriages I believe) are quickly becoming dirty, tatty, and showing signs of neglect and abuse. Seats tend to be quite cramped, and it is not uncommon to have to stand, especially for passengers boarding at intermediate stops like Newry and Portadown. All this at the not-so-cheap price of £40.00 stg for a standard return (although it can be as "low" as £20 at certain times). Frankly, I prefer to take the bus which can be about 30 minutes longer but more comfortable, you are guaranteed a seat with a ticket and at a fraction of the price. It also stops at DUB, and uses stations in the centre of the city (as opposed to using the airports)