How the relative importance of community assembly processes varies with spatial scale is the focus of intensive debate, in part because inferring the scales at which specific niche-based processes act is difficult. One obstacle is that standard phylogenetic and functional diversity metrics may integrate the signals of multiple processes when combining separate niche axes into one variable (multiple-niche-axis metrics), potentially obscuring overlapping niche-based processes. We use simulations to evaluate the power of these metrics to detect competition and habitat filtering when these processes operate across multiple niche axes and vary in their relative importance. We then test for both processes at a range of spatial scales in a Neotropical bird assemblage. Simulations revealed that multiple-niche-axis metrics had low power to detect competition and habitat filtering when a mix of both processes acts across niche axes, whereas metrics focused on single-niche axes were better able to deal with this complexity. We found the same contrast in bird communities, where both competition and habitat filtering were detected at the scale of individual territories, but only by single-niche-axis metrics focused on specific niche axes (e.g., foraging traits). Our results suggest that multiple-niche-axis metrics may produce misleading evidence that niche-based processes are partitioned, particularly across scales, and highlight the importance of analyzing functional diversity patterns on individual niche axes when testing assembly models.