When is paying more for an airport transfer actually worth it?

The train may be much cheaper, but a fare comparison does not account for everything. Heavy bags, several changes, an early departure, or traveling with someone who finds long walks difficult can change the calculation. On the other hand, an expensive transfer is not automatically the easiest option either.

How do you weigh cost against effort for airport journeys? Interested in examples where a little planning made public transport straightforward, and situations where a direct ride earned its price. Include the number of travelers and the time of day so the comparison has some shape.