fairytale is right - it all depends on your class. We have flown twice PE and four times Economy, using DTD check-in for all of them. The queues in economy have ranged from 15mins to just over an hour and every where in between. We do try to get there before 9am though.
The trouble for economy passengers is that PE, Upper Class and Gold FC have priority boarding over economy. So if the economy line is 7 families deep, and a PE customer arrives, they get seen to first, have bags weighed then sent straight to the desk, bypassing all those 7 families in the Economy queue.
We do DTD check-in these days because 1) we fly PE so it's quick anyway, and 2) because we usually have to speak to someone about the seating arrangements, because no matter how many times I call Special Assistance and no matter how many notes we have on file, the return flight never seem to be able to handle the requests as well as going out. Guess there are just more restrictions or whatever, but being there at 8:15am gives us a bit of an advantage over those checking in later at DTD or even at the airport.
Plus, we can fill out all the wheelchair/special assistance forms there and then, which just removes one more thing we would have to do at the airport otherwise.