Budget LAX became corporate a couple years ago. Not sure if the fleet is pooled with Avis or not. Note that Budget SAN and Budget LAS are still franchises. Proceed with caution at both, especially SAN.

Budget LAX was one of the few "Fast Break Choice" locations I have seen (had it back when it was a franchise too). Vehicles in the lot by car class and the shuttle stopped you at your assigned area. Not sure how it worked on a specialty vehicle but for me reserving an economy I always had a large selection of late model farily low mileage bare bones compacts to select from in my assigned area then go to the booth to complete the rental and get the contract.

For a premium vehicle, I think I'd go with Avis over Budget. Personally as one who reserves compacts I'd go with Budget over Avis to save the 5% if it was a bare bones rental I was expecting/looking for.