With the continuous spread of new SARS-CoV-2 variants of concern (VOCs), the monitoring of diagnostic test performances is mandatory. We evaluated the changes in antigen diagnostic tests’ (ADTs) accuracy along the Delta to Omicron VOCs transition, exploring the N protein mutations possibly affecting ADT sensitivity and assessing the best sampling site for the diagnosis of Omicron infections. In total, 5175 subjects were enrolled from 1 October 2021 to 15 July 2022. The inclusion criteria were SARS-CoV-2 ADT combined with a same-day RT-PCR swab test. For the sampling site analysis, 61 patients were prospectively recruited during the Omicron period for nasal and oral swab analyses by RT-PCR. Next-Generation Sequencing data were obtained to evaluate the different sublineages. Using RT-PCR as a reference, 387 subjects resulted in becoming infected and the overall sensitivity of the ADT decreased from 63% in the Delta period to 33% in the Omicron period. This decrease was highly statistically significant (p < 0.001), and no decrease in viral load was detected at the RNA level. The nasal site presented a significantly higher viral load than the oral site during the Omicron wave. The reduced detection rate of Omicron infections by ADT should be considered in the global testing strategy to preserve accurate diagnoses across the changing SARS-CoV-2 variants.