Prescription medication, whether antibiotics or something else, are typically of higher quality than over-the-counter drugs due to the fact that over-the-counter drugs are typically made very cheaply to be bought cheaply. So thus a prescription specific medication will typically be of higher quality. This is why we need universal healthcare.
Whether they are sold with or without a prescription, antibiotics carry the same risks and have the same side effects. The advantage to over the counter sale of antibiotics is that it makes this important medication available to those that have less access to healthcare and would lower the prices by allowing store brands to develop.