Micropollutants have been increasingly detected at low concentrations in surface waters and may have harmful effects on humans, organisms, and the environment. As wastewater treatment plants are one of the main sources of micropollutants, conventional wastewater treatment methods and plants (mainly one to three cleaning stages) must be improved through an advanced (fourth) treatment stage. The optimal fourth treatment stage should be determined based not only on removal efficiencies but also on a holistic sustainability assessment that further considers the process’s adaptability, economic, environmental, and social parameters. The ability of a tertiary wastewater treatment plant to remove organic pollutants was investigated over four months using two different advanced treatment methods: (1) an advanced oxidation process (AOP) (using UV + H2O2) and (2) granular activated carbon (GAC). The resulting average micropollutant removal efficiencies were 76.4 ± 6.2% for AOP and 90.0 ± 4.6% for GAC. As the GAC became saturated, it showed a decreasing performance from 97.6% in week one to 80.7% in week 13, after 2184 bed volumes were processed. For the AOP, adjusting the UV and H2O2 doses results in higher removal efficiencies. With 40 ppm H2O2 and 10 kJ/m2 UV, a removal of 97.1% was achieved. Furthermore, the flexibility and adaptability of the AOP process to adjust to real-time water quality, along with a lower resource consumption and waste disposal, make it a more promising technology when comparing the sustainability aspects of the two methods.