Yes, if you are able to do so. Most public defenders (PD) I know are very good attorneys. However, they simply have too many cases through no fault of their own. Sometimes, as many as 100-150 at any given time.
If you want somebody to walk you through the DUI Court Process as well as the DOL process and always be accessible - it is usually better to obtain private counsel, if at all possible. (I give my clients my cell phone number - no other attorney in my office does that!) We have all been to a restaurant where the waiter or waitress were serving many many more tables then he or she should have been. As a result, things just didn't go as smoothly as we may have liked. It is the same thing with private attorneys - I am serving only so many clients at a time and therefore able to provide more personal attention to your DUI case and specific needs or considerations. I have many clients who would be eligible for the PD, but instead make small monthly payments to my office. (Also, the PD can not represent you in the Civil Administrative Department of Licensing Hearing.)