Their style could hardly be more different, though their aims are the same: as Greta Thunberg sailed into New York last week on a low-carbon high-tech yacht to highlight the climate crisis, Prince Harry faced flak for taking private jets for short-hop breaks while campaigning against global heating. But the contrast between the two reflects broader dilemmas in the environmental movement.

On Tuesday, the Duke of Sussex invited further ridicule as he flew into Amsterdam – a direct Eurostar train from London takes three hours and 41 minutes – to unveil an initiative for the tourism industry, Travalyst, which aims to reduce the impact of holidaymakers but encourages travel.

Harry defended his flying record on the basis that “nobody is perfect”, and that “occasionally [there is] a unique circumstance to ensure that my family are safe”.

The Guardian recently calculated, using data from the German NGO Atmosfair, that a UK citizen taking a single flight can have the same impact on the climate in a few hours as a person in one of the world’s least developed countries does in a whole year. For the prince, travel by private plane for his family is likely to generate as much as an entire village.

But not everyone can solve their travel problems like Thunberg, as there is unlikely to be a transatlantic sailing boom to replace flying.

Tony Juniper, one of the UK’s most prominent environmentalists who has worked with Prince Charles and now chairs Natural England, said the prince was not alone in facing green dilemmas.

“Prince Harry does a great deal of good work raising awareness and helping to make progress on conservation questions,” he said. “Like anyone else, however, he has to deal with the circumstances of the real world, and the fact that we don’t yet have zero-emissions planes. Flying less is certainly a key message we all need to hear but quite a lot of environmentalists use planes to make their work possible, and in his position he often has no alternative but to fly, including for reasons of security.”

The irony of encouraging tourism, despite its potential damage to pristine or struggling environments, and the emissions involved in getting to remote places, is also one that the green movement must grapple with, Juniper said.

“Ecotourism is one of the ways that wildlife can be rendered worth more alive than dead, and it is something the conservation community needs to embrace as one strategy alongside others,” he said.

“Take the example of Costa Rica, where deforestation has been reversed, in large part because of the economic benefits that come with tourists visiting to see the wonderful wildlife there.”

The royals’ fellow feeling for other endangered creatures is certainly valued by the organisations they work with. Mark Jones, the head of policy at Born Free, which campaigns for wildlife, said: “The interest the royal family, and particularly princes William and Harry, have shown in global wildlife conservation has undoubtedly helped bring the plight of wildlife to the attention of a truly global audience, from decision-makers to the wider public. We are grateful for their interest in and support for our efforts to reverse global biodiversity loss and provide a secure future for the wildlife with which we share our world.”

Greenpeace says it would like to see a frequent flyer levy, tax on aviation fuel, an end to airport expansion and most of all moves to rein in demand, because strategies such as offsetting – donating cash to programmes that reduce greenhouse gas emissions in other areas – are not enough.

John Sauven, executive director of Greenpeace UK, said: “Offsetting works over an extremely long timeframe. Maybe as a way of raising money for reforestation it works, but that’s charity. We should call it what it is.”

Justin Francis, a co-founder of the travel firm Responsible Travel, said: “Voluntary [offsetting] initiatives are not enough – the cost of flying must increase. Carbon offsets are no substitute for carbon reduction.”

Anna Hughes, who runs the campaign group Flight Free UK, said: “The answer is simply not to fly.”

Flying has expanded rapidly in recent years, partly owing to tax breaks and incentives compared with less carbon-intensive travel, and last year accounted for 2.6% of energy-related emissions.

On Friday, new details of the Sussexes’ forthcoming Africa tour will be revealed by Buckingham Palace. It is believed that conservation and green issues will be among the top priorities for the couple’s first major overseas programme of engagement, as well as gender equality, education and development, where the duchess has already made a mark.

The British royal family is not alone in striving to save the planet, as monarchies across Europe have taken to espousing environmental programmes as a way to bring their influence to bear on intractable problems – and incidentally to maintain high-profile roles and win popular support without courting political controversy.

The Dutch royal family campaigns on water scarcity and flooding, Prince Albert of Monaco has taken a leading role in marine conservation, including battling plastic pollution, and the Nordic royals highlight the dangers to the Arctic from global heating.

There have been missteps along the way, though, and not just for Harry – in 2014 his elder brother, William, was roundly criticised for shooting wild boar and deer with Spanish royals the day before launching a wildlife appeal.