My general rule of thumb is that with one, the car is roughly on-par with the train, once parking has been taken into account. But once two or more are travelling the car becomes more attractive. If flights are between 0500 and 0900 though, it can be hard to get to the airport in sufficient time, if travelling with checked in baggage.
I don't think Train Vs Car is a set decision for all journeys. If there are 4/5 of us travelling and I can get a multi-story car park for a good price, then the car is a no-brainer. If its just me, travelling with only hand luggage, coming off a night shift the train is likely to be a more attractive option.