We analyze JWST Mid-Infrared Instrument/Medium Resolution Spectrograph integral field unit observations of three Seyferts from the Galactic Activity, Torus, and Outflow Survey (GATOS) and showcase the intriguing polycyclic aromatic hydrocarbon (PAH) and emission-line characteristics in regions of ∼500 pc scales over or around their active galactic nuclei (AGN). Combing the measurements and model predictions, we find that the central regions containing a high fraction of neutral PAHs with small sizes, e.g., those in ESO137-G034, are in highly heated environments, due to collisional shock heating, with hard and moderately intense radiation fields. Such environments are proposed to result in inhibited growth or preferential erosion of PAHs, decreasing their average size and overall abundance. We additionally find that the central regions containing a high fraction of ionized PAHs with large sizes, e.g., those in MCG-05-23-016, are likely experiencing severe photoionization because of the radiative effects from the radiative shock precursor besides the AGN. The severe photoionization can contribute to the ionization and further destruction of PAHs. Overall, different Seyferts, even different regions in the same galaxy, e.g., those in NGC 3081, can contain PAH populations of different properties. Specifically, Seyferts that exhibit similar PAH characteristics to ESO137-G034 and MCG-05-23-016 also tend to have similar emission-line properties to them, suggesting that the explanations for PAH characteristics of ESO137-G034 and MCG-05-23-016 may also apply generally. These results have promising application in the era of JWST, especially in diagnosing different (i.e., radiative and kinetic) AGN feedback modes.