Multiphase flows in wellbores and pipes can be described within the framework of two major approaches, namely, the multi-fluid approach and the driftflux approach. The fundamental difference between the approaches is in the formulation of the momentum conservation equations in the mathematical model. Within the multi-fluid model, a set of mass and momentum conservation equations is written for each phase in the continuum approximation, while the drift-flux model offers a single momentum equation for the mixture as a whole in terms of the volume-averaged velocity of the mixture. Both approaches require closure relations derived from and tuned with respect to laboratory data. In this work, we compare both approaches and apply them to solve the transient problem of terrain induced slugging relevant to the field of well testing and production and compare performance of the models.