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In this paper, I contrast two broad decompositional approaches to verb semantics. One, especially associated with David Dowty, involves translating verbs using a set of precisely interpreted primitive predicates such as cause and become, in order to facilitate semantic generalizations such as patterns of entailment between sentences. Another, with multiple origins in both temporal semantics and theories of the syntax/semantics interface (including, notably, work by Pustejovsky and Piñón), involves developing a theory of the internal part structure of the eventualities that verbs and other expressions describe; I refer to this approach, following Pianesi and Varzi, as mereotopological. These two approaches to decomposition are not, strictly speaking, incompatible, and they have sometimes been combined; however, perhaps surprisingly, comparison of them has been unsystematic. I address this gap by describing more systematically how the approaches differ from each other, illustrating with differences in the insights they offer into specific aspects of the semantics of simple change of state verbs and unselected object resultatives. I especially aim to promote interest in the development of more sophisticated, cross-linguistically applicable theories of so-called event structure through appeal to a wider range of notions from mereotopology.