Weighted model counting (WMC) is an extension of propositional model counting with applications to probabilistic inference and other areas of artificial intelligence. In recent experiments, WMC algorithms are shown to perform similarly overall but with significant differences on specific subsets of benchmarks. A good understanding of the differences in the performance of algorithms requires identifying key characteristics that favour some algorithms over others. In this paper, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We then use this model to experimentally compare the performance of WMC algorithms c2d, Cachet, d4, DPMC, and miniC2D on random instances. We show that the easy-hard-easy pattern is different for algorithms based on dynamic programming and algebraic decision diagrams (ADDs) than for all other solvers. We also show how all WMC algorithms scale exponentially with respect to primal treewidth and how this scalability varies across algorithms and densities. Finally, we demonstrate how the performance of ADD-based algorithms changes depending on how much determinism or redundancy there is in the numerical values of weights.