The importance of high intensity few- to single-cycle laser pulses for applications such as intense isolated attosecond pulse generation is constantly growing, and with the breakdown of the monochromatic approximation in field ionization models, the few-cycle pulse (FCP) interaction with solids near the damage threshold has ushered a new paradigm of nonperturbative light-matter interaction. In this Letter, we systematically study and contrast how femtosecond laser-induced damage and ablation behaviors of SiO2/HfO2-based reflective multilayer dielectric thin film systems vary between FCP and 110 fs pulses. With time-resolved surface microscopy and ex situ analysis, we show that there are distinct differences in the interaction depending on the pulse duration, specifically in the "blister" morphology formation at lower fluences (damage) as well as in the dynamics of debris formation at higher fluences (ablation).