ProM. I worked at Heathrow most of my life and I have visited LAX many times so I am fairly familiar with both airports. There are various ways that the "busy" factor is determined - by passengers, freight, aircraft movements, etc. I always think in terms of aircraft movements which I believe is the true indication of how "busy" a place is and LAX shifts considerably more aircraft in 24 hours than Heathrow. Last year LAX was running at about 1700 movements per day, a bit down on the previous year. By comparison, the Heathrow figure was around 1300 per day.
BAA always claims that Heathrow is the "World's Busiest", but that's only good for international passengers. In that respect I believe it even betters O'Hare... but O'hare has well over twice as many aircraft movements per day than Heathrow.