The three main options, ranked by cost
A medical escort on a scheduled flight is the least expensive: commercial fares for patient and escort, the clinician's time and travel, and ground transport. A commercial airline stretcher sits in the middle, because the airline blocks multiple seats for the installation. A dedicated air ambulance is the most expensive, because you are paying for the aircraft, its crew and its positioning.
What is included in a proper quote
Air transport, medical crew and equipment, ground ambulance at both ends, permits and handling where applicable, and any accommodation or duty-time cost from overnight stops. If a quote omits ground legs, the real cost will be higher than the number you were given.
Insurance and who pays
Travel insurance, credit-card travel cover, employer programs and government arrangements are the common funding sources. Insurers normally require prior approval and their own medical assessment. If cover is declined or absent, the family pays privately, in which case the choice of transport option matters even more.
Where the cost can be reduced
Waiting until a patient is stable enough for an escorted commercial flight, travelling on a route with better carrier options, and allowing enough lead time to avoid an immediate positioning flight can all reduce cost substantially, where the clinical picture allows it.