A couple of examples from my side.
2003 we went with a big tour operator, we came out of the airport told our reps we didn't need their
transfer services as we had booked privately with ICR, we arrived at apartments around 4.30am, the following day we found people on our flight who arrived at 07:00am
In 2007 we went DIY and had to use a private transfer, coming home a family left our
hotel 2 hours before us for the journey to the airport (Different flight than our but only by 15 minutes), they were with a TC coach transfer and they were the first pickup, we beat them to the airport by 20 minutes with a private transfer.
Private transfers are definately the way to go, no hanging around for people at the airport and no drop offs or pickups.
Dave