Agroforests are of well-known importance for biodiversity conservation, especially in the tropics, because they are structurally stable and may resemble natural forests. Previous studies have characterized jointly taxonomic, functional and phylogenetic diversity in these agro-ecosystems to comprehensively examine the mechanisms by which agriculture impacts on biodiversity. However, this approach has been barely applied to other woody crops of economic importance, such as olive grove, which is a remarkable overwintering habitat for frugivorous/insectivorous birds from central and northern Europe, and whose original distribution overlaps with the Mediterranean biodiversity hotspot. We examined the effects of landscape complexity and intensive management practices at a local scale (recurrent plowing and pesticides use) on the functional and phylogenetic diversity of animal communities inhabiting olive groves. Since the response of functional traits or clades may vary across different taxonomic groups, we conducted our study at two levels: ants, which are considered semi-sessile organisms, and birds, which exhibit a high dispersal capacity. In birds, neither management type nor landscape complexity had an effect on phylogenetic diversity (PD) indices. Extensively managed farms harbored bird communities with higher values of functional diversity (FD), but this effect only was evident when considering cultivated (productive) zones within the farm (i.e., infield diversity). Ant assemblages on intensively managed farms exhibited a lower level of phylogenetic clustering than those located in extensive farms, but this effect vanished when excluding non-cultivated zones. Ant functional diversity increased with landscape complexity. Our results indicate that PD and FD exhibit different responses to farming intensification in olive groves. Although intensive management does not erode PD due to the existence of phylogenetic redundancy, the loss of species associated to modern farming leads to a reduction in FD being this indicative of functional complementarity. This study provides evidence that land-use extensification (extensive farming and landscape diversification) promotes more functionally rich assemblages than modern intensive practices in olive groves. Our findings also show the need to set apart the effect of non-cultivated zones (e.g., hedgerows, margins) when evaluating the effectiveness of agri-environment schemes as the joint consideration of non-cultivated and cultivated areas may obscure the benefits of local extensification on infield biodiversity.