Convicts in private prisons serve 90 days longer than public prisons
This is about 5% longer.
In private prisons, the company's contract has it that they are payed a per diem for each occupied bed.
"The delayed release erodes half of the cost savings offered by private contracting and is linked to the greater likelihood of conduct violations in private prisons. The additional days served do not lead to apparent changes in inmate recidivism," according to the author.*
Mukherjee, Anita. "Impacts of Private Prison Contracting on Inmate Time Served and Recidivism."