A comparison of different model simulations of the ionosphere variability during the 2009 sudden stratosphere warming (SSW) is presented. The focus is on the equatorial and low‐latitude ionosphere simulated by the Ground‐to‐topside model of the Atmosphere and Ionosphere for Aeronomy (GAIA), Whole Atmosphere Model plus Global Ionosphere Plasmasphere (WAM+GIP), and Whole Atmosphere Community Climate Model eXtended version plus Thermosphere‐Ionosphere‐Mesosphere‐Electrodynamics General Circulation Model (WACCMX+TIMEGCM). The simulations are compared with observations of the equatorial vertical plasma drift in the American and Indian longitude sectors, zonal mean F region peak density (NmF2) from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites, and ground‐based Global Positioning System (GPS) total electron content (TEC) at 75°W. The model simulations all reproduce the observed morning enhancement and afternoon decrease in the vertical plasma drift, as well as the progression of the anomalies toward later local times over the course of several days. However, notable discrepancies among the simulations are seen in terms of the magnitude of the drift perturbations, and rate of the local time shift. Comparison of the electron densities further reveals that although many of the broad features of the ionosphere variability are captured by the simulations, there are significant differences among the different model simulations, as well as between the simulations and observations. Additional simulations are performed where the neutral atmospheres from four different whole atmosphere models (GAIA, HAMMONIA (Hamburg Model of the Neutral and Ionized Atmosphere), WAM, and WACCMX) provide the lower atmospheric forcing in the TIME‐GCM. These simulations demonstrate that different neutral atmospheres, in particular, differences in the solar migrating semidiurnal tide, are partly responsible for the differences in the simulated ionosphere variability in GAIA, WAM+GIP, and WACCMX+TIMEGCM.