Having done all three during my last trip back to the UK.
Gatwick Express by far the worst. Travelled from Airport to Victoria. Extremely overcrowded. Ticketing at the airport abysmal. Ride uncomfortable and appalling. Baggage space - dreadful. An embarrassment. Cost - decent.
Next would be Stansted. Travelled from Liverpool street to the Airport. Ticketing easy, train carriages good and not over-crowded, ride so-so. Baggage space - satisfactory. Cost - good.
Heathrow Express. Travelled both ways to and from Paddington. Quite spacious, decent and modern seating. Speedy journey both ways. Plenty of ticketing at airport and at Paddington. Ride good, comfortable. Bad side having to cross to another platform for terminal 4, and hauling your bags through those restrictive barriers. Baggage space on train: excellent. Cost: Over-expensive but much better designed rolling stock, seating and baggage space make it worth while and so much better to get to London than the Tube.
My experience of airports overseas in recent years:
Singapore: Regular trains from the airport, but having to change after the first station is a huge bore and there is no express into the centre of the city.
Kuala Lumpur. Very good service fast, though a little expensive but cost can be lowered by booking on-line. Baggage space a little on the short side.
Bangkok: Modern, fast, empty. It goes nowhere where passengers want to get to. Taxi's so much easier, even during the cities traffic jams, even if you take the train to a city centre station, and jump into a taxi to complete your journey.
Port Moresby: No trains in the entire nation. such a sadness.