Yes, they usually price Avis a bit (or sometimes a lot) higher than Budget, but once you start applying discount and coupon codes (even publicly available ones), you never know which one will end up being a better deal.

Also keep in mind that in some locations (LAS for example), Budget is a licensee whereas Avis is corporate, so rates are set independently there, and you could certainly end up with a situation where Avis is lower than Budget even for rack rates.