Conceptualising landscapes as a mosaic of discrete habitat patches is fundamental to landscape ecology, metapopulation theory and conservation biology. An emerging question in ecology is: when is the discrete patch model more appropriate than alternative and conceptually appealing models such as the continuum model? There is limited empirical testing of the utility of alternative landscape models compared to the discrete patch model for a range of species. In this paper, we constructed three alternative sets of models for testing the effect of landscape structure on diversity and abundance of a suite of woodland birds in a savanna landscape of northern Australia: the null model (only site-scale habitat variables, landscape context not important), the continuum model, and the discrete patch model. We utilised high-spatial resolution satellite images to quantify spatial gradients in tree cover density (the continuum model), and to then aggregate the fine-scale heterogeneity in tree cover into discrete patches of trees, with grass cover forming the “matrix” (the discrete patch-model). We then evaluated the relative importance of the alternative models using generalised linear models and an information theoretic approach. We found that the importance of the models varied among species, with no single model dominant. Species that move between open grassy areas and woody shelter responded well to the continuum model, reflecting the importance of gradients in density of forage (grasses) and cover (trees), while the discrete model performed best for species that forage in all vegetation strata, and nest predominantly in dense woody vegetation. This finding supports a pluralistic approach, highlighting the need for adopting and testing more than one landscape model in savanna landscapes, and in other landscapes that do not have a well defined patch structure.