We investigate information transmission in neuronal models based on Brownian motion and the Ornstein–Uhlenbeck process, in which neuronal spiking times are modeled as first passage times through oscillating boundaries. Using both mutual information and mutual information per unit time as metrics, we analyze how boundary oscillation parameters and input variability influence coding efficiency. Our analysis reveals complex dependencies on input variability and diffusion strength, including non-monotonic effects of input variance and unexpected increases in information with diffusion strength in the Ornstein–Uhlenbeck case. We also identify the existence of optimal oscillation frequencies, whose values depend on the specific information measure used.