I went through last year and things have not changed. I transfered from Air NZ to Air Canada and the process took about 2 hours. Im glad our connecting flight did not leave for 12 hours.
I then tried SFO about a month later with the same airlines and we were through in about 1/2 hour.
I know it comes down to volume (the same time we landed there was a Virgin 747 and I think a Qantas 747) in LAX but if you can avoid it by going through SFO or even YVR I think all involved - including those working at LAX - would be most happy!
Just imagine when those 747's start becoming A380's.........