We compare designs and laser-induced damage thresholds (LIDTs) of hafnia/silica antireflection (AR) coatings for $1054\mathrm{nm}$ or dual $527\mathrm{nm}/1054\mathrm{nm}$ wavelengths and $0°$ to $45°$ angles of incidence (AOIs). For a $527\mathrm{nm}/1054\mathrm{nm}$ , $0°$ AOI AR coating, LIDTs from three runs arbitrarily selected over three years are $\sim 20\mathrm{J}/{\mathrm{cm}}^2$ or higher at $1054\mathrm{nm}$ and $<10\mathrm{J}/{\mathrm{cm}}^2$ at $527\mathrm{nm}$ . Calculated optical electric field intensities within the coating show two intensity peaks for $527\mathrm{nm}$ but not for $1054\mathrm{nm}$ , correlating with the lower (higher) LIDTs at $527\mathrm{nm}$ ( $1054\mathrm{nm}$ ). For $1054\mathrm{nm}$ AR coatings at $45°$ and $32°$ AOIs and S and P polarizations (Spol and Ppol), LIDTs are high for Spol ( $>35\mathrm{J}/{\mathrm{cm}}^2$ ) but not as high for Ppol ( $>30\mathrm{J}/{\mathrm{cm}}^2$ at $32°$ AOI; $\sim 15\mathrm{J}/{\mathrm{cm}}^2$ at $45°$ AOI). Field intensities show that Ppol discontinuities at media interfaces correlate with the lower Ppol LIDTs at these AOIs. For Side 1 and Side 2 dual $527\mathrm{nm}/1054\mathrm{nm}$ AR coatings of a diagnostic beam splitter at $22.5°$ AOI, Spol and Ppol LIDTs ( $>10\mathrm{J}/{\mathrm{cm}}^2$ at $527\mathrm{nm}$ ; $>35\mathrm{J}/{\mathrm{cm}}^2$ at $1054\mathrm{nm}$ ) are consistent with Spol and Ppol intensity behaviors.