Fluorescence Imitating Brightfield Imaging (FIBI) represents an innovative approach in microscopy, providing real-time, non-destructive imaging of tissue without the need for the preparation of thin sections mounted on glass slides. The non-destructive nature of the technology permits tissue preservation for downstream analysis, which makes FIBI a promising alternative to traditional hematoxylin and eosin (H&E) staining in histopathology. Previous research has shown that FIBI can identify morphological features with similar or, in some cases, higher quality compared with H&E images. To comprehensively quantify the advantages and limitations of FIBI in tissue visualization, we propose a novel framework for characterizing the topological difference of FIBI and H&E slide pairs. Experiments are performed on slide pairs of FIBI and H&E imaging of the same tissue area. The proposed approach shows that FIBI can make morphological structures, like vessels, more salient and holds great promise as a complementary technique to H&E, offering novel insights into tissue architecture and potentially improving histopathological diagnostic accuracy.