Both candidates also spoke about their plans for stepped up prosecution of criminals and how they will handle the political pressures of the job.
Both women have criminal justice backgrounds. Anderson has filled several roles in the courtroom as a prosecutor, felony court judge and defense attorney.
Ogg was also a prosecutor and became the city's gang task coordinator, running Crime Stoppers of Houston, and spent many years as a defense attorney.
A major point of contention will most likely be the jailing of assault victims and destroyed evidence by the Harris County Precinct 4 constable's office.
The embattled district attorney is facing harsh criticism after a rape victim was put in jail when prosecutors were unsure if she would testify. Her office is reviewing almost 22,000 pieces of evidence that were destroyed by Precinct 4 since 2007.
The debate will be held at the Windsor Village United Methodist Church in the Kingdom Builder's Center on Orem Drive.