Prices being equal choose Avis over Budget as Avis is the premium brand while Budget is the discount brand. The service can be better at Avis and the cars newer, but it's very much a YMMV situation.

The big advantage of choosing Avis over Budget, especially at an airport location, is that you can enroll in Avis Preferred (free to join) and skip the rental counter. Budget has a somewhat similar service called FastBreak but the Avis program is much more seamless and the points you earn, while not particularly valuable, are certainly more valuable than the crappy Budget Bucks certificates they issue.

In short, choose Avis over Budget at the same or similar price and sign up for Avis Preferred.

PS--AutoSlash can search for discounted rates at all companies including Avis and Budget, and if you're a member of Avis Preferred or Budget FastBreak, you can enter your member number on the checkout page to get all the benefits like skipping the counter, earning points, etc.