Multiparental populations (MPPs) encompass greater genetic diversity than traditional experimental crosses of two inbred strains, enabling broader surveys of genetic variation underlying complex traits. Two such mouse MPPs are the Collaborative Cross (CC) inbred panel and the Diversity Outbred (DO) population, which are descended from the same eight inbred strains. Additionally, the F1 intercrosses of CC strains (CC-RIX) have been used and enable study designs with replicate outbred mice. Genetic analyses commonly used by researchers to investigate complex traits in these populations include characterizing how heritable a trait is, i.e., its heritability, and mapping its underlying genetic loci, i.e., its quantitative trait loci (QTLs). Here we evaluate the relative merits of these populations for these tasks through simulation, as well as provide recommendations for performing the quantitative genetic analyses. We find that sample populations that include replicate animals, as possible with the CC and CC-RIX, provide more efficient and precise estimates of heritability. We report QTL mapping power curves for the CC, CC-RIX, and DO across a range of QTL effect sizes and polygenic backgrounds for samples of 174 and 500 mice. The utility of replicate animals in the CC and CC-RIX for mapping QTLs rapidly decreased as traits became more polygenic. Only large sample populations of 500 DO mice were well-powered to detect smaller effect loci (7.5-10%) for highly complex traits (80% polygenic background). All results were generated with our R package musppr, which we developed to simulate data from these MPPs and evaluate genetic analyses from user-provided genotypes.