There is large uncertainty whether Amazon forests will remain a carbon sink as atmospheric CO2 increases. Hence, we simulated an old‐growth tropical forest using six versions of four terrestrial models differing in scale of vegetation structure and representation of biogeochemical (BGC) cycling, all driven with CO2 forcing from the preindustrial period to 2100. The models were benchmarked against tree inventory and eddy covariance data from a Brazilian site for present‐day predictions. All models predicted positive vegetation growth that outpaced mortality, leading to continual increases in present‐day biomass accumulation. Notably, the two vegetation demographic models (VDMs) (ED2 and ELM‐FATES) always predicted positive stem diameter growth in all size classes. The field data, however, indicated that a quarter of canopy trees didn't grow over the 15‐year period, and while high interannual variation existed, biomass change was near neutral. With a doubling of CO2, three of the four models predicted an appreciable biomass sink (0.77 to 1.24 Mg ha−1 year−1). ELMv1‐ECA, the only model used here that includes phosphorus constraints, predicted the lowest biomass sink relative to initial biomass stocks (+21%), lower than the other BGC model, CLM5 (+48%). Models projections differed primarily through variations in nutrient constraints, then carbon allocation, initial biomass, and density‐dependent mortality. The VDM's performance was similar or better than the BGC models run in carbon‐only mode, suggesting that nutrient competition in VDMs will improve predictions. We demonstrate that VDMs are comparable to nondemographic (i.e., “big‐leaf”) models but also include finer scale demography and competition that can be evaluated against field observations.