I got stopped for DUI by a City of Marietta police officer. I heard that I can ask for my case to be heard in Cobb County instead of the City of Marietta Court. What's the difference and what do you recommend?

There are many factors to consider when you are trying to decide whether  to take your case to the State Court of complete it in the City court and you must talk to an experienced attorney who is familiar with each court in order to make the correct decision.  Briefly, if you want to enter a guilty plea to the charge, you may want to enter into plea negotiations with the City Court. If you want to contest your case and have a jury trial, then your case must be transferred to the State Court as the City Court usually does not have the authority to conduct jury trials.