Three hours, 44 minutes: that is how long it took by train to get from St Pancras International station in London to Amsterdam in the Netherlands. I paid £35 for a seat aboard the inaugural Eurostar rail departure from the UK to the Dutch capital.

A couple of minutes after the Amsterdam Express arrived, I was admiring the handsome facade of Centraal station. The visionary architect was Pierre Cuypers, who also designed the city’s Rijksmuseum: he saw mass transportation and fine art as equally deserving of grand design.

I had little time to appreciate the gracious structure, though. I was heading straight back to St Pancras – the hard way, by plane. I wanted to see how long it took to link the same points as the train, but in a much straighter line: flying from Schiphol airport to Gatwick.

Remarkably, the answer was three hours, 44 minutes.

It might look like a tie, but the plane wins. Here’s how. The flying time included arriving at the airport an hour ahead of departure. But 224 minutes for the the train journey didn’t take into account the half-hour check-in requirement for Eurostar (in Business Premier, it’s down to 10 minutes).

Yet the smooth rail experience put into sharp relief the clunky nature of 21st-century aviation. Some high-tech tweaks and low-tech sense could have made flying so much better.

When I booked the flight the night before, for a very reasonable €58 (£52), British Airways tried to sell me a hotel and car rental in London, simply obstacles to my online progress. What BA didn’t offer was a rail ticket from Amsterdam to Schiphol or from Gatwick to London.

I defer to IT boffins on how that might work. But since both airport links are high-frequency, no-advance-booking trains, it appears to a mere traveller that selling an e-ticket (with a pound or two premium for the time-saving) might not be that tricky. And if I bought one, a bit more software might enable British Airways to see I was booked on the 2.50pm flight, and send a quick note saying: “We recommend that you catch the 1.31pm, which normally leaves from platform 11b.”

Or if easyJet got there first with such useful embellishments, I would be tempted to book from the orange kingdom with the orange airline.

Schiphol is a great transit airport and wins lots of awards. (Perhaps that’s why the UK Department for Transport used a picture of it to illustrate Friday’s press release about aviation security.) But it gets no prize from me for clarity.

In common with perhaps one-third or half of passengers starting their journey from Schiphol airport, I had already checked in. All I wanted to see at the airport railway station was a screen telling me the gate number, or at least an indication of the area of the huge terminal to aim for, plus a big sign pointing to the appropriate security channel. Instead, I was despatched to BA check in, from where it was not at all obvious or intuitive where I needed to go.

After a half-hour route march (partially through poor wayfaring on my part), I was relieved to board the plane, and experience what I expect will be the closest I get to an upgrade this year: an instantly wider seat. I was sitting in 5F, two rows behind the business-class curtain. Seat 5E was empty, and the cabin service manager demonstrated how on that particular Airbus A320, some of the forward rows have moveable armrests which expand the size of your seat (so to speak).

BA’s new location at Gatwick South Terminal should appeal to time-pressed travellers because it removes the extra few minutes involved in getting the North Terminal shuttle. Even though the aircraft tied up at the furthest possible gate from passport control, I thought I had a sporting chance of catching a train 10 minutes after arrival. But then I saw the queue for immigration, and that only 10 of 25 e-passport gates were working.

Gatwick now offers “premium passport control”, offering a fast track for £7. But anyone with a train to catch who is tempted to jump the queue needs to have registered online between six months and four hours in advance. Turning up with a credit card is not acceptable. The train to St Pancras left while I was halfway along the slow-moving line.

Had I caught the train, the rail/plane/rail combo would have comfortably won the race. Which, as you may already have concluded, was an artificial construct.

There are very many reasons why, even if your travel plans involve Amsterdam, the train is irrelevant. Unless you live within reasonable reach of London, it will save cash as well as time to fly: the Dutch capital is the best-connected foreign city from the UK, with links from 25 airports.

And even if you are going from London to Amsterdam, the number of real people (ie not Eurostar staff) who will ever want to travel exactly from St Pancras to Centraal station is vanishingly small.

Most of us want to get from home or work to hotel or business location. And that shifts the balance even further in favour of aviation, especially since Londoners have six airports from which to choose, and many businesses and hotels in Amsterdam are on the Schiphol side of town.