This paper presents a theoretical framework to analyze the relative merits of the two most general, dominant approaches to speaker diarization involving bottom-up and top-down hierarchical clustering. We present an original qualitative comparison which argues how the two approaches are likely to exhibit different behavior in speaker inventory optimization and model training: bottom-up approaches will capture comparatively purer models and will thus be more sensitive to nuisance variation such as that related to the speech content; top-down approaches, in contrast, will produce less discriminative speaker models but, importantly, models which are potentially better normalized against nuisance variation. We report experiments conducted on two standard, single-channel NIST RT evaluation datasets which validate our hypotheses. Results show that competitive performance can be achieved with both bottom-up and top-down approaches (average DERs of 21% and 22%), and that neither approach is superior. Speaker purification, which aims to improve speaker discrimination, gives more consistent improvements with the top-down system than with the bottom-up system (average DERs of 19% and 25%), thereby confirming that the top-down system is less discriminative and that the bottom-up system is less stable. Finally, we report a new combination strategy that exploits the merits of the two approaches. Combination delivers an average DER of 17% and confirms the intrinsic complementary of the two approaches.