Summary Wood performs several functions to ensure tree survival and carbon allocation to a finite stem volume leads to trade‐offs among cell types. It is not known to what extent these trade‐offs modify functional trade‐offs and if they are consistent across climates and evolutionary lineages. Twelve wood traits were measured in stems and coarse roots across 60 adult angiosperm tree species from temperate, Mediterranean and tropical climates. Regardless of climate, clear trade‐offs occurred among cellular fractions, but did not translate into specific functional trade‐offs. Wood density was negatively related to hydraulic conductivity (K_th) in stems and roots, but was not linked to nonstructural carbohydrates (NSC), implying a functional trade‐off between mechanical integrity and transport but not with storage. NSC storage capacity was positively associated with K_th in stems and negatively in roots, reflecting a potential role for NSC in the maintenance of hydraulic integrity in stems but not in roots. Results of phylogenetic analyses suggest that evolutionary histories cannot explain covariations among traits. Trade‐offs occur among cellular fractions, without necessarily modifying trade‐offs in function. However, functional trade‐offs are driven by coordinated changes among xylem cell types depending on the dominant role of each cell type in stems and roots.