It can be done in both, however you have to be careful when deciding your surgeon and do your homework.At an accredited surgical center you will have a board certified anesthesiologist supervising your anesthesia. In order to have privileges in a surgery center you need to have the the proper training for the procedure, and be a board certified surgeon or board eligible surgeon. "Cosmetic" surgeons and dermatological surgeons are not real plastic surgeons and they can not perform these aesthetic surgeries in real surgical centers or hospitals, so it is always a good idea to ask the surgeon if you have the option to have the surgery done in a recognized surgery center other than the office.In some states, nurse anesthetist can perform your anesthesia without anesthesiologist ( MD) supervision, these will be cheaper but arguably less safe. In summary, check the credentials of your surgeon and also the details of who is performing your anesthesia. A surgery center will always have more resources than a office base center, in the rare cases of emergencies, due to the high volume of cases they perform.