This study presents a benchmark of two physics-guided neural surrogates – PhyCNN and multi–LSTM – across three single-degree-of-freedom system scenarios of increasing nonlinearity: (I) a Duffing oscillator; (II) a hysteretic Bouc–Wen system under band-limited noise; and (III) a hysteretic Bouc–Wen isolator representative of base-isolated buildings subjected to long-duration Chilean earthquakes. Physics-guided LSTMs achieve the lowest errors in displacement and velocity and better reproduce hysteretic geometry; CNNs yield tighter, more stable errors when the normalized internal force is predicted directly. Reconstructing force from LSTM velocity closes much of the gap but remains fragile in long, strongly nonlinear records due to residual-drift accumulation. Simple training discipline—input/target normalization, validation-driven early stopping and scheduling, and light force regularization—substantially improves robustness.