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Climate, species composition, and soils are thought to control carbon cycling and forest structure in Amazonian forests. Here, we add a demographics scheme (tree recruitment, growth, and mortality) to a recently developed non-demographic model—the Trait-based Forest Simulator (TFS)—to explore the roles of climate and plant traits in controlling forest productivity and structure. We compared two sites with differing climates (seasonal vs. aseasonal precipitation) and plant traits. Through an initial validation simulation, we assessed whether the model converges on observed forest properties (productivity, demographic and structural variables) using datasets of functional traits, structure, and climate to model the carbon cycle at the two sites. In a second set of simulations, we tested the relative importance of climate and plant traits for forest properties within the TFS framework using the climate from the two sites with hypothetical trait distributions representing two axes of functional variation (“fast” vs. “slow” leaf traits, and high vs. low wood density). The adapted model with demographics reproduced observed variation in gross (GPP) and net (NPP) primary production, and respiration. However, NPP and respiration at the level of plant organs (leaf, stem, and root) were poorly simulated. Mortality and recruitment rates were underestimated. The equilibrium forest structure differed from observations of stem numbers suggesting either that the forests are not currently at equilibrium or that mechanisms are missing from the model. Findings from the second set of simulations demonstrated that differences in productivity were driven by climate, rather than plant traits. Contrary to expectation, varying leaf traits had no influence on GPP. Drivers of simulated forest structure were complex, with a key role for wood density mediated by its link to tree mortality. Modeled mortality and recruitment rates were linked to plant traits alone, drought-related mortality was not accounted for. In future, model development should focus on improving allocation, mortality, organ respiration, simulation of understory trees and adding hydraulic traits. This type of model that incorporates diverse tree strategies, detailed forest structure and realistic physiology is necessary if we are to be able to simulate tropical forest responses to global change scenarios.