Medical image segmentation in laparoscopic surgery is challenging due to the high cost of pixel-level annotations and the need for domain expertise. In this paper, we investigate how Active Learning (AL) strategies perform across four laparoscopic video datasets that vary in two critical characteristics: (1) redundancy vs. diversity in their frames, and (2) balanced vs. imbalanced distributions of anatomical objects. We compare purely uncertainty-based approaches, purely diversity-based approaches, and hybrid strategies that combine both. Experimental results demonstrate that datasets containing many consecutive, visually similar frames hamper uncertainty-based AL methods, as these methods repeatedly select near-duplicate samples. In contrast, diverse datasets, especially those with balanced object frequencies, enable uncertainty-based methods to excel by focusing on hard or rare samples. For datasets with imbalanced object distributions, hybrid approaches prove particularly beneficial by capturing both model-driven uncertainty and underrepresented objects. Overall, our findings indicate that the choice of AL strategy should be carefully aligned with the inherent structure of a dataset, and that combining diversity and uncertainty often yields the most robust performance across various laparoscopic surgery scenarios. Our code is publicly available on https://github.com/amiiiirrrr/AL4LS .