What about Newark? I went through Newark Penn Station a few times and it seems decent. Is it a PITA to go between Newark Penn Station and the airport, or is the airport itself a bigger hassle than most?

Last time I went through LAX there were no good options for getting from there to downtown LA.

Newark is probably the least bad, but you still have to take a slow second train (AirTrain) after getting to Newark Penn. Also, while the NJ Transit trains are better set up for travelers than the LIRR to JFK they aren’t nearly as nice as the dedicated setup they have in London.

Although Heathrow Express is quite pricey compared to the tube and, depending upon where you're going, may not even be more convenient. More often than not, I'm near Trafalgar Square so I just take the Piccadilly Line in. But, yes, Heathrow has good transit options in general (although it's an expensive cab ride).