Managed forests are a key component of strategies aimed at tackling the climate and biodiversity crises. Tapping this potential requires a better understanding of the complex, simultaneous effects of forest management on biodiversity, carbon stocks and productivity. Here, we used data of 135 one-hectare plots from southwestern Germany to disentangle the relative influence of gradients of management intensity, carbon stocks and forest productivity on different components of forest biodiversity (birds, bats, insects, plants) and tree-related microhabitats. We tested whether the composition of taxonomic groups varies gradually or abruptly along these gradients. The richness of taxonomic groups was rather insensitive to management intensity, carbon stocks and forest productivity. Despite the low explanatory power of the main predictor variables, forest management had the greatest relative influence on richness of insects and tree-related microhabitats, while carbon stocks influenced richness of bats, birds, vascular plants and pooled taxa. Species composition changed relatively abruptly along the management intensity gradient, while changes along carbon and productivity gradients were more gradual. We conclude that moderate increases in forest management intensity and carbon stocks, within the range of variation observed in our study system, might be compatible with biodiversity and climate mitigation objectives in managed forests.