For the record, I live in London, but I travel to NYC for business every once in a while (I am actually a qualified attorney in NYS). This is a bit of an odd one - the fact that you are throwing random statistics at me from wikipedia or wherever really just demonstrates that you do not understand either of these cities. People in finance from Europe and other parts of the world flock to London because it is the financial center of Europe; and, equally, people from the US and other parts of the world flock to NYC because it is the financial center of the Americas. These two cities are the two global places to be for finance and related activities. The resulting effect of this is that both cities have their share of resulting industries and related cost factors which by far exceed national averages, i.e. London accounts for about 22% of the UK's total GDP, I am used to paying £7+ for a pint and double that for cocktails, I spend £20+ a day on lunch, etc.
The reason why NYC has a higher population density than London is because NYC is a city of skyscrapers whereas in London there are relatively few of these. The reason for that is because most properties in London are covered by restrictive covenants which prohibit building height exceeding that of its neighbors and in practice makes commercial real estate in London exceedingly expensive. But, no-one says: "I am going to NYC instead of London because the population density is higher." When it comes to green areas, NYC practically only has Central Park, whereas London has Green Park, Hyde Park, Richmond, Kew Gardens, Hampstead Heath, etc. But, no-one says: "I am going to London instead of NYC because I want to hang out in Hyde Park". Literally same for your murder rate, cost of a bottle of water (who gives a fuck?) and rent, etc. Several years ago I had a catch-up with a friend who had just moved over from JPM in London to NYC. Even though her headline salary nearly doubled, her verdict was that after she pays off her rent in Hell's Kitchen, her health insurance and her yoga lessons and other miscellaneous expenses, she has the same amount of money left in her account as she used to in London.
What you need to understand is that the relevant comparison for these two cities is not the people who live and work in Queens vs the ones who live and work in Zone 8, it's the people who are live and work in Manhattan vs Zone 1 - and on all such comparable metrics they are broadly the same. I personally prefer London because of the history and the culture - both of these are lacking in NYC by comparison. There are others who disagree, but that disagreement is not down to the cost of a fucking bottle of water.