The Amex Centurion Card offers guaranteed vehicle availability with both Hertz and Avis. I would consider that to be an elite-type perk, albeit "comped" elite.

Hertz #1 sends coupons to members, although I think that everyone gets the same coupons whether they rent frequently or not.

And I am also one of the (few?) remaining members of the original National Car Rental Emerald Club, and I earn Emerald Club points for my rentals in addition to miles. Since you can no longer enroll in the points program, I guess the program qualifies as "elite."