Depends.
Emirates and some of the Asian airlines like Cathay Pacific that do long haul routes are very good for service. For solid transatlantic flight service: Lufthansa, British Airways, Virgin are pretty good. American and Delta take service up a notch on translantic routes, but not much. I flew Berlin Air recently, which I think is newer, it was very nice.
On major US routes, Delta seems to be doing the best job and has upgraded most of it's terminal space lately, even in NYC. Jet Blue, on many of its routes does a very good job and has the benefit like some of the smaller airlines of not having a work force that has been disgruntled for the last 20 years like American, United, AA/USAirways. In general all the surviving, major US airlines have flight crews who hate their flying just as much as their passengers.