Compared to real cellular systems where users are spatially distributed and interference levels vary by several orders of magnitude over a cell, in the Wyner model user locations are fixed and the interference intensity is characterized by a single fixed parameter. Although it is a fairly extreme simplification, the Wyner model has been extensively used to analyze cellular networks. Does it capture some of the main trends of such networks or not? In this study of downlink cellular networks, we show that from an outage point of view, the Wyner model is highly inaccurate since outage is primarily a function of user location. However, in the case of average throughput, the Wyner model may in some special cases be an acceptable simplification if the interference parameter is set appropriately. In particular, we show that it is relatively accurate in terms of the average throughput for CDMA systems with single-cell processing and perfect channel inversion, and for the sum throughput of multicell processing with equal transmit power per user. In short, the Wyner model appears to be a reasonable approximation for SINR mean-based metrics like sum and average throughput for certain scenarios, but is unreasonable in nearly all cases for SINR tail-based metrics like outage probability.