Via HyperAllergic, the above image was created by LA-based artist Zach Alan, who superimposed Manhattan on a map of LA's galleries and other cultural institutions. The map of LA art fails to note outdoor art, such as murals and installations, but does show the vastness of Los Angeles and demarcates where our "art clusters" are, mainly Culver City, Hollywood, and Downtown. None of those clusters approaches the level of density in one NYC neighborhood (shown in red).
It's not controversial to note that the New York City gallery-based art scene is older, larger, and more sophisticated than its equivalent in LA. It's also much denser, with Chelsea alone having over 200 galleries in a walkable area. Some would argue that this density is what makes the scene so successful, as art buyers and artists alike can bounce from gallery to gallery in a single night, being exposed to more art in a few hours than you could ever get in any one part of Los Angeles. This leads some to conclude, falsely, that LA's art scene is not reaching its potential because of its geography.
Even the proudest New Yorker would agree that the issue with LA isn't a lack of amazing art and artists. Many have noted the westward move of former NYers seeking better weather, more space, and the ability to create a personal reality that isn't constrained by the overwhelming nature of NYC's urban rhythm-- in short, "sprawl" has its benefits to artists and other creative people even as it potentially separates them from each other. So when comparing NY to LA, the spread-out nature of the city is a bit of a red herring, especially because there clearly are artistically dense parts of the city.
The real problem facing LA's art scene is that it's (relatively) young, immature, and underdeveloped. The art clusters in our city, such as Culver and DTLA are too new, and need more interesting galleries, non-profits, parties/fairs/exhibitions/performances. Moreover LA needs more patrons who are willing to get our of their houses and support the arts scene on a regular basis. In short, density as a whole is not the issue, it's about the networks of support our art clusters are currently getting. We can and should have a few "Chelseas" in LA. Better transportation would certainly help (one of the first comments in the Hyper Allergic thread mentions free wine, which isn't advisable in a car-centric city); more city involvement in promoting the arts would help; a comprehensive mural policy that would allow the city to reclaim its title as the mural capitol of the world would certainly help focus LA's strengths.
Rather than make apples to oranges comparisons to New York's geography and vibrant gallery scene, Angeleños should look to the future and how we can realize, on the gallery and public art end, what we already have in terms of quality and diversity of art. Several nodes, each with their own mini-scene and focus, can and will develop in LA's vast network of creativity if the city's artists and art lovers work together to make it happen.