The fares side by side
A car from Haddenham takes up to 4 passengers, so eight people need two cars. To Heathrow, that means two fares of £85, or £170 one way. The 8 seater minibus taxi takes the same eight people for £139. To Gatwick, two cars cost £230 and the minibus costs £180. To Luton, two cars cost £130 and the minibus costs £127.
Luggage
Each car takes up to 3 large suitcases, so two cars take 6 between them. The 8 seater minibus taxi takes up to 10 large suitcases. For a family going on holiday, that is usually what decides it.
Travelling together
In one vehicle, the whole group leaves and arrives at the same time. Nobody waits at the terminal for the second car. There is one driver to call if anything changes.
When the 6 seater taxi is the better choice
For 5 or 6 people with up to 3 large suitcases, the 6 seater taxi costs less than the minibus. To Heathrow, it is £124 compared with £139. If you have more than 3 large suitcases, book the minibus.