Owing to their relatively high resistance to laser-induced damage, hafnia and silica are commonly used in multilayered optical coatings in high-power laser facilities as high- and low-refractive-index materials, respectively. Here, we quantify the laser-induced-damage threshold (LIDT) at 1053 nm in the short-pulse regime of hafnia and silica monolayers deposited by different fabrication methods, including electron-beam evaporation, plasma ion-assisted deposition and ion-assisted deposition. The results demonstrate that nominally identical coatings fabricated by different deposition techniques and/or vendors can exhibit significantly different damage thresholds. A correlation of the LIDT performance of each material with its corresponding absorption edge is investigated. Our analysis indicates a weak correlation between intrinsic LIDT and the optical gap of each material (Tauc gap) but a much better correlation when considering the spectral characteristics in the Urbach tail spectral range. Spectrophotometry and photothermal absorption were used to provide evidence of the correlation between the strength of the red-shifted absorption tail and reduced LIDT at 1053 nm.