Accurately projecting population size is key to population and conservation ecology, but accurate predictions remain elusive beyond 1-2 years. Matrix projection modeling (MPM) approaches are commonly used, including Leslie and Lefkovitch models, empirical and function-based MPMs, age-by-stage and historical MPMs, with and without density dependence. We used individual-based demographic datasets of five perennial herbs, each covering 20-36 years, to compare the accuracy of these approaches, splitting each dataset into model building and prediction subsets. We developed each model using a simple vs complex life history, with and without climate predictors, characterizing model accuracy against observed population dynamics. Lefkovitch models outperformed Leslie and age-by-stage models. Function-based models (complex IPMs) predicted observed population dynamics more accurately than empirical models. Among stage-based models, historical models predicted most accurately. Density dependence increased accuracy in all cases. We suggest that individual history and density dependence should be more broadly incorporated into studies of population dynamics.