My cousin in Mesa had a DUI case last year and went with the private lawyer for three grand. The public defender got a better deal for the guy next to him in court, same charges. It really depends on the PD you get, but a lot of them know the local prosecutors and judges way better than some hired gun. I'd only pay up if it was something really serious.
That $5,000 price tag for a lawyer in Phoenix is wild to me. Miles798 has a point about public defenders knowing the local system, so I get your choice. Honestly, I'd probably do the same thing unless it was life or death.