Parametrically driven oscillators exhibit distinct dynamical regimes that strongly influence their computational capability as physical reservoirs. Here, we demonstrate reservoir computing in a two-mode system exhibiting 2:1 parametric resonance using Mackey--Glass, Rössler, and Lorenz chaotic time-series prediction tasks. Mapping the normalized mean squared error over parameter space reveals that the lowest prediction errors consistently occur within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states increase spectral dimensionality, prediction performance degrades in the chaotic comb regime due to loss of phase coherence. We further show that the modulation depth $Δ\text{F}$, detuning $κ$, damping ratio $γ_{21}$, and input data rate systematically reshape the accessible dynamical regimes and thereby control the reservoir performance. These results identify parametric resonance as a robust operating regime for oscillator-based neuromorphic computing and establish dynamical regime engineering as a route toward physical reservoir optimization.

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