That immigration chart is slightly skewed as London freely takes immigrants from the entire EU while NYC takes far less immigrants because of US Immigration policy. If I had to choose I'd probably say NYC would be "greatest" although I don't even know where to begin to describe the criteria. London I'd give credit to as the metropolis of the great British Empire of which us Americans are essentially a spawn of. Historically speaking NYC can't even compete with the influence of London save for the last few decades. I think you are all forgetting one city....ROME. The heart of everything western no other city had such impact on the world. Roman (well often techincally Greek) architecture is prominent in every gov't building in both London and New York. That's not even scratching the surface as Rome had sanitation and water systems 2000 years ago that were better than NYC's in the 1900s. To me "greatness" means "might" and Rome, London, and New York are the great cities of the world's (former and current) empires. Think about if NYC had remained the capital of the US, no city could ever rival that kind of power.
Wow, it must mean that London is better. Honestly, I cannot go a week without meeting a Britisher who wants to move to the USA, or somewhere warm like Thailand or Australia. Was that chart supposed to mean something to us? In respect of property prices, big deal. Literally, Big Deal. Especially in London, its a Big Deal for the agents who are getting rich. The increase is an aberration based on the fact that people can borrow more money more cheaply; sellers therefore will ask a higher price. It doesn't mean anything. From another perspective, would you prefer to live in London, or say, a tropical paradise like Bora Bora? Property is much cheaper in Bora Bora, and you have a lot more beach too. High prices on paper don't mean anything except for people who own property and think that they can justify borrowing more to finance cars, holidays and other consumables just because there is a bubble.