Based on my experience with both (I rent nowhere near as much as others on this forum) Avis tend to upgrade me for free more than Hertz ever did.

I used to manage to get Hertz to upgrade me from a full size booking to a Volvo XC70 (which they categorise as a prestige car) but it is not as nice as a CTS nor has as much power. But that was a few years back - since then it has been Mercury Sables (ok car, a bit anonymous though), a Ford Edge (I don't like that SUV at all - the brakes are so weak) and the last one was a Avalon with about a million miles on it (felt like it was going to break).

I did manage to get Hertz in LAX to give me a brand new (less than 100 miles on the clock) Infiniti M35 in Jan 08 though - that was very nice! - but had to pay around $100 over the full size booking I had to secure it though - it was a 4 day rental.

Plus for me as I am based in the UK, Avis is cheaper - book on avis.co.uk to get the all inclusive price.