Hospital wastewater is harmful to the environment and human health due to its complex chemical composition and high potency towards becoming a source of disease outbreaks. Due to these complexities, its treatment is neither efficient nor cost-effective. It is a challenging issue that requires immediate attention. This effort focuses on the treatment of hospital wastewater (HWW) by removing two selected drugs, namely ibuprofen (IBU) and ofloxacin (OFX) using individual biological treatment methods, such as moving bed biofilm reactors (MBBR) and physicochemical treatment, such as ozonation and peroxane process. The both methods are compared to find the best method overall based on effectiveness and removal efficiency. The optimal removal for ozone dosing range was nitrate (9.00% and 62.00%), biological oxygen demand (BOD) (92.00% and 64.00%), and chemical oxygen demand (COD) (96.00% and 92.00%) that required at least 10 min to reach considerable degradation. The MBBR process assured a better performance for ibuprofen removal, overall. The IBU and OFX removal was found to be 14.32–96.00% at a higher COD value and 11.33–94.00% at a lower COD value due to its biodegradation. This work strives to pave the way forward to build an HWW treatment technology using integrated MBBR processes for better efficiency and cost-effectiveness.