Hi Mark Diver,
Neither LAX or BUR has a priority security line for HP passengers.
I would suggest that you fly into the airport that is closer, giving a 15 minute premium toward BUR. If it would take 15+ extra minutes to drive to your destination from BUR, I'd probably just choose LAX. At this point, the problem (in time differential between LAX and BUR) isn't so much with the security lines, it's the traffic backup around LAX (BUR never has this).
In my recent experience with BUR and LAX (flying HP), the lines haven't been too bad. However, LAX does have the potential to get much worse than BUR.
With a reasonably precise location of your destination, I may be able to offer more/better advice. Since I don't know where you are headed, this is the best I can do!
Later,
Tim in Hollywood