In this work, we prove that, for a current regime of 10 μA and using industry‐relevant programming pulse‐width, Cu/Al2O3‐based conductive‐bridging RAM (CBRAM) cells ensure reliably larger memory window (MW) than state‐of‐the‐art oxygen‐vacancy‐based RRAM (OxRRAM) cells. Due to the intrinsically stochastic nature of the switching mechanism, the Ron and Roff values can be widely distributed, especially in a low‐current regime, drastically reducing the overall memory window. For this reason, in this study we adopt a statistical approach, focusing on the tails of the distributions. Using a program‐verify method we show that the larger median MW in CBRAM allows to program a MW ≥×10 using ×10 shorter programming time with respect to OxRRAM. Moreover, we show that, in order to ensure a MW >×10 after a fixed retention time, the programming time needs to be several decades larger for OxRRAM than for CBRAM.