Artificial injections of sulfur dioxide (SO2) into the stratosphere show in several model studies an impact on stratospheric dynamics. The quasi-biennial oscillation (QBO) has been shown to slow down or even vanish under higher SO2 injections in the equatorial region. But the impact is only qualitatively but not quantitatively consistent across the different studies using different numerical models. The aim of this study is to understand the reasons behind the differences in the QBO response to SO2 injections between two general circulation models, the Whole Atmosphere Community Climate Model (WACCM-110L) and MAECHAM5-HAM. We show that the response of the QBO to injections with the same SO2 injection rate is very different in the two models, but similar when a similar stratospheric heating rate is induced by SO2 injections of different amounts. The reason for the different response of the QBO corresponding to the same injection rate is very different vertical advection in the two models, even in the control simulation. The stronger vertical advection in WACCM results in a higher aerosol burden and stronger heating of the aerosols and, consequently, in a vanishing QBO at lower injection rate than in simulations with MAECHAM5-HAM. The vertical velocity increases slightly in MAECHAM5-HAM when increasing the horizontal resolution. This study highlights the crucial role of dynamical processes and helps to understand the large uncertainties in the response of different models to artificial SO2 injections in climate engineering studies.