Having a Catholic Pope and the General Secretary of the Communist Party of China descend on Washington at almost exactly the same time helped illustrate something important about diplomacy. When staging a high-level state visit, there is a simple choice: emphasise either the head or the heart. This is especially the case if it concerns the US and China, where the relationship evades simple rational descriptions. Almost invariably, despite its risks, appealing to the heart brings better returns. 

Yet President Xi almost entirely missed that opportunity.

Xi Jinping after the White House Rose Garden joint press conference. (Win McNamee/Getty.)

True, in terms of hard political outcomes, President Xi's US sojourn achieved its objectives. There was a solid agreement on the environment, some progress on trade and a little (but enough) on cyber security. But the curious thing about Xi's intensely managed and controlled visit is the way it illustrates just how profoundly conservative Chinese diplomacy is, and how poor it is at conveying one of the most exciting and dynamic stories of our age – China's transformation.

Xi is a better communicator than his predecessor, Hu Jintao. He laced his Seattle speech with nice popular touches, even describing the current anti-corruption struggle in China as 'no House of Cards.' But the promise of this speech, and the expectations in terms of public diplomacy of the visit overall, quickly dissipated.

His meeting with technology companies in Seattle was symptomatic. Sitting prominently on the podium beside Xi after listening to the President's peroration on the importance of technology and creativity was Mark Zuckerberg, the creator and owner of Facebook, whose wildly successful website is famously blocked in China. A picture circulated afterwards of Zuckerberg shaking Xi's hands, while Lu Wei, China's top internet regulator, stood smiling in between. Were Chinese officials trying to convey some point about how even those it paints as threats have, in the end, to come and bid obeisance? This messaging might play well as a display of power in China. For Americans, however, it was portrayed in the press as ironic and controlling, never the best way to an audience's heart.

Xi did no walkabouts where he might have slightly less scripted encounters with the American public. He had a couple of staple visits to a school and a factory, but there was nothing in these to fire the imagination. For this, we have to look at the master of public appeals, Pope Francis, whose frugal use of a simple Fiat car for transport, and stopping to bless a boy with cerebral palsy, proved stories too good to keep off the US front pages. The Chinese Communist Party propaganda department really needs to look at the skill of this remarkable leader and take some lessons.

Complaining about a biased Western press cuts no mustard here. This press is free. Ways can be found to get China's message across, and the Pope has shown that, even heading an organisation emerging from one of the worst scandals imaginable, he can still get its core messages across. 

The Chinese Government might argue that in the end their main priority is to use the US trip for messaging back home. And there, of course, it saturated the media, night and day. But one has to have the sneaking suspicion that they will be a little disappointed that Xi wasn't able to reach out directly to the American people the way his wife did, just through using decent English when speaking on women's education at the UN. 

Talking directly to the American people through their media, and through a more spontaneous kind of visit, would be a massive asset for China. Like it or not, this is an audience they cannot ignore. American presidents can come to China and reach out over the heads even of managed media, gathering popular plaudits. China's Ministry of Foreign Affairs, by contrast, shows itself once more to be one of the most cautious and risk averse in the world. Management and control remain their main objectives, not trying to reset the attitudes towards their country by more creative visit programs by one of their key assets – their national leader. Symptomatically, Xi's 'interview' in the Wall Street Journal turned out to be responses to queries submitted in writing, raising questions about just how much input the President even had in the answers finally published. 

It doesn't need to be this way. Deng Xiaoping in the early 1980s had extensive interviews with journalists like Oriana Fallaci from Italy and Mike Wallace from CNN. Jiang Zemin did the same. Jiang was even willing to sprinkle his speeches with English, Russian and French. It's odd that President Xi's visit did not take a few more risks.

The visit to the US did have things the wider American public, and in the rest of the world, need to be aware of: huge moves on climate change, and a lot of recognition of common trade and security challenges. But on the whole, the person best placed to speak about these issues and promote recognition of them, Xi himself, was confined behind a wall of minders and protocol. The question impossible to answer now is whether this is because of a failure of imagination by those serving him, which can be rectified by making them think more boldly, or whether it is because of the President himself. That would be a far harder problem to address.