We consider the task of glomeruli segmentation from Whole-Slide Images (WSIs) of pathological kidneys. In particular, we compare the performance of two different encoder-decoder architectures for two tasks: local segmentation of patches extracted from a large WSI, and global segmentation of the entire image. Since segmenting high-resolution WSIs is extremely memory-demanding, a typical approach for this task is to break down these images offline, train a patch-wise segmentation model, and then use a sliding-window inference scheme to stitch back the resulting patch segmentations. Contrary to intuition, we observe in our experiments that a model with higher segmentation accuracy at the patch level can incur in large underperformance gaps at the WSI level, even more so when measuring performance as an instance segmentation problem. This work was carried out in the context of the Kidney Pathology Image Segmentation (KPIs) challenge, which took place jointly with MICCAI 2024, and the best patch-level model we present here ranked second in the final hidden test set of the competition. Code to reproduce our experiments is shared at github.com/agaldran/kpis .