Diagnostic science assessments seek to draw inferences about student understanding by eliciting evidence about the mental models that underlie students' reasoning about physical systems. Measurement techniques for analyzing data from such assessments embody one of two contrasting assessment programs: learning progressions and facet-based assessments. The research presented here provides a systematic comparison of these two approaches, which is of great practical value to assessment programs that seek to employ small clusters of related items for the purpose of measuring depth of understanding. Specifically, models were compared on model-data fit, diagnostic reliability, diagnostic certainty, and predictive accuracy. In addition, the effects of test length were evaluated for both models in order to inform the number of items required to obtain adequately reliable diagnoses of understanding. Lastly, changes in student understanding over time were studied with a longitudinal model in order to provide educators and curriculum developers with a sense of how students advance in understanding over the course of instruction.