Dense active matter is gaining widespread interest due to its relevance in biology, offering a novel statistical-physical framework to describe and understand the complex dynamics of confluent cell layers and tissues. Curiously, dense disordered active systems show remarkable similarities with inanimate disordered (glassy) materials, including dynamical signatures reminiscent of a liquid-to-glass transition. However, it has remained notoriously unclear how non-equilibrium activity changes the glassy behavior, since different studies have reported either a speedup, slowdown, or non-monotonic change of the relaxation dynamics. Here we rationalize these seemingly conflicting results in an unambiguous manner. Specifically, using computer simulations of active model glass-formers, we find that active glassy matter exhibits an optimum in the dynamics when the active persistence length equals the glassy cage length, i.e. the length scale of local particle caging. The ratio between the persistence length and the cage length thus acts as a unifying control parameter for the dynamics. We also provide a simple physical argument for this new finding, and demonstrate its generality and robustness for both thermal and athermal active systems, for both active Brownian and Ornstein-Uhlenbeck particles, and for both hard and soft active particles. Overall, our work reconciles and explains the manifestly disparate results reported previously in literature, and reveals a hitherto unknown universal feature in the behavior of dense disordered active matter.