Before take-off, the airline has the best estimate (not that it isn't often wrong, but the FAA data is irrelevant for the most part). Sometimes you'll see the FAA flight plan data show a delayed take-off time before departure due to a ground delay program or ground stop, but that isn't consistent (although worth checking).
Once the plane is in the air, Flightaware / Flightview / et al use ASDI data from the FAA to place it. It's expected landing time (wheels down) is generally a pretty good estimate at that point. The airline arrival time should be a few minutes after that to account for taxiing. If it's not, I'd trust the FAA data over the airline data.