Being both a US-based Avis Presidents Club and Hertz Presidents Circle member, the upgrade / recognition benefits are significantly better with Avis - I typically get a luxury car assigned, however Hertz rarely gives me anything other than what I have booked. The Avis customer service (on the phone and at the branches) is also significantly better.

The only thing going for Hertz is their rewards program, I earn free rental days significantly faster in Hertz's program (especially during promotions - where I tend to earn enough points for 2 free weekend days for each weekly rental).