This paper examines two classes of algorithms that estimate a continuous time ARX type of models from discrete data: one is based on infinite impulse response (IIR) filters while the other is based on finite impulse response (FIR) filters. The IIR filters use continuous time state variable filters, and discretisation is performed on the filtered derivatives. In contrast, the FIR filters are in a discrete form with carefully chosen coefficients to approximate the derivatives of the continuous time variables. The strength and weakness of each approach are discussed and demonstrated by a set of simulation examples.