Automatic segmentation of cell nuclei clusters is a key building block in systems for quantitative analysis of microscopy cell images. For that reason, it has received a great attention over the last decade, and diverse automatic approaches to segment clustered nuclei with varying levels of performance under different test conditions have been proposed in literature. To the best of our knowledge, however, so far there is no comparative study on the methods. This study is a first attempt to fill this research gap. More precisely, the purpose of this study is to present an objective performance comparison of existing state-of-the-art segmentation methods. Particularly, the impact of their accuracy on classification of thyroid follicular lesions is also investigated quantitatively under the same experimental condition, to evaluate the applicability of the methods. Thirteen different segmentation approaches are compared in terms of not only errors in nuclei segmentation and delineation, but also their impact on the performance of system to classify thyroid follicular lesions using different metrics (e.g., diagnostic accuracy, sensitivity, specificity, etc.). Extensive experiments have been conducted on a total of 204 digitized thyroid biopsy specimens. Our study demonstrates that significant diagnostic errors can be avoided using more advanced segmentation approaches. We believe that this comprehensive comparative study serves as a reference point and guide for developers and practitioners in choosing an appropriate automatic segmentation technique adopted for building automated systems for specifically classifying follicular thyroid lesions.