You have to keep in mind that when it comes to thinking about the environment, it gets really complicated. It’s not a matter of energy used/person, there are other factors to keep in mind. Consider this:
Are we comparing when they are both full or when they are empty? Because the carbon footprint of your journey is also dependent on how many other people are sharing the transport with you. If we talking strict averages, based on data from 2008, London Underground’s carbon footprint was equivalent to approx. 93 grammes CO2 per passenger kilometre. Alternatively, a typical Euro III double deck with a diesel particulate filter produces 1384.3 grammes CO2 per kilometre – so if you’ve got more than 15-20 people on the bus, then it would be more or less the same. However – test results vary from real life. More people on the bus = more weight, more traffic = more carbon emitted, longer stopping at bus stops = more carbon, and finally it even depends on how quick the bus driver accelerates.
What do you mean by “sustainable” – Are you looking at carbon emissions? Because if so you need to look beyond the journey itself and at the emissions caused for the entire process. Your journey is only possible because a train/bus and all its components had to be designed, built, assembled, exported, and finally put into use and maintained.
"You need to factor the total lifecycle of each the tube/bus and its components and then divide it per number of people it takes over the entire lifecycle. This has not been done and is not easy to do."
What about the resources? Minerals, metals, water, land are all important components that factor into sustainability – it’s not all about carbon. What materials have been used in the construction and maintenance of the whole system? How were they extracted? What happens to these resources afterwards?
You need to also consider the infrastructure system. So while roads use resources to be constructed and maintained, they are not constructed only for busses. Cars, motorcycles, bicycles, and others use these roads. For the subway, the tunnels, and the emissions used to construct the system, is only borne by the tube. The resources, energy, and other costs in the original construction also need to be factored in.
In short – public transport is better than taking a private car, but stick to walking/cycling if you really want to be sustainable. Even then, you got to think about how you are getting your calories back, because if you eat a meat-heavy diet, then the environmental damage from growing food for these lot calories outweighs the emissions saved by walking.