Depends where your final destination is going to be but as has been mentioned, the Airlink uses the port tunnel whereas the Aircoach travels in on the N1 via Drumcondra to the north of the city centre.
Timewise there isn't much in it. The Aircoach claims around 25 minutes from the airport to O'Connell Street in the centre of town. The Airlink is 30 to BusÁras (main bus station) which is next to Connolly Station, and a further 10minutes to O'Connell Street.
Expect this to be longer for both during rush hour though, possibly as much as 50 minutes to an hour!
Aircoach is 12 return to the city centre (more if you're heading on to Sandyford) on the day or 11 if you book online.
Airlink is 10 return.
If you're staying on the Southside of the city, the Aircoach may well be the option you want as that goes on through Sandyford or Ballsbridge. If you're using those, make sure you get the right bus!
My first trip to Dublin years ago, started with a terrifying ride on the Aircoach as we hurtled through roadworks and crowded streets. Sadly, the AerDART option ceased in 2007 I think. This involved getting the DART out to Howth Jcn, then hopping on a bus to the airport.