It is determined by the surgeon or the policy of his hospital urology team but no, it isn't usually based on the patient's recuperation. Usually, there is a standard position - at the hospital where my husband had his op it is 10 days, some urologists prefer 7 days or to wait the full 14 days. At a hospital where the prostatectomies are done on Wednesdays and TWOC clinic is on a Friday, all men will be called for their catheter removal 9 days post op. At a hospital where the catheter is removed by the urology nurse or surgeon, it might be any day of the week.
The judgment about personal recovery comes at TWOC time - if the catheter is removed but the patient cannot pass urine, the catheter is put back in for another week or more. They can't tell how well the join has recovered until they take the catheter out and ask you to try it.