Read: Cities Without Suburbs: Census 2000 Update. It has a good comparison of northeast and southwest city sprawl.
Outside of New England, Metro areas are not officially defined by commute patterns, they are simply taken to be the entire county. In new england, it is different. So, to compare densities of Boston and L.A., you would need to introduce an element of similarity. I propose this should be comparing the L.A. county with Suffolk county (that's the county Boston is in, right?). Well, which one is denser...then you have your answer. Of course Boston will be denser right now, as things are currently considered, because its metro encloses a primarily urban area, but in L.A. it is different due to different regional census rules, so large areas of wilderness that have nothing to do with the city are included. Just the urbanized section of L.A. and its surroundings is probably denser than Boston, if only because of the poor and rushed planning and development characteristic of an area like So Cal that has more people coming in than leaving.
Lastly, L.A. is not the only metro in the world increasing in density. Any metro area that adds population yearly gains density. I believe this includes boston.