To contribute to a quantitative comparison of climate engineering (CE) methods, we assess atmosphere-, ocean-, and land-based CE measures with respect to Earth system effects consistently within one comprehensive model. We use the Max Planck Institute Earth System Model (MPI-ESM) with prognostic carbon cycle to compare solar radiation management (SRM) by stratospheric sulfur injection and two carbon dioxide removal methods: afforestation and ocean alkalinization. The CE model experiments are designed to offset the effect of fossil-fuel burning on global mean surface air temperature under the RCP8.5 scenario to follow or get closer to the RCP4.5 scenario. Our results show the importance of feedbacks in the CE effects. For example, as a response to SRM the land carbon uptake is enhanced by 92Gt by the year 2100 compared to the reference RCP8.5 scenario due to reduced soil respiration thus reducing atmospheric CO2. Furthermore, we show that normalizations allow for a better comparability of different CE methods. For example, we find that due to compensating processes such as biogeophysical effects of afforestation more carbon needs to be removed from the atmosphere by afforestation than by alkalinization to reach the same global warming reduction. Overall, we illustrate how different CE methods affect the components of the Earth system; we identify challenges arising in a CE comparison, and thereby contribute to developing a framework for a comparative assessment of CE.