This paper compares the identification of step response model coefficients based on either an autoregressive moving average (ARMA) model or a unit pulse response model. The identification of the two model types is compared for speed and accuracy in achieving the ideal step response coefficients in open-loop and closed-loop single-input, single-output systems. This comparison is useful for those wishing to construct an adaptive form of those model-based predictive controllers that use an internal step response process model.