Mitochondrial network structure is controlled by the dynamical processes of fusion and fission, which merge and split mitochondrial tubes into structures including branches and loops. While it is common for work examining fusion or fission to be motivated by the regulation of protein spread through mitochondria by these dynamical processes, there is only limited quantitative work connecting network dynamics to spread efficiency. We included particle diffusion for stochastic simulations of two distinct quantitative models that each included mitochondrial fusion and fission. Better-connected mitochondrial networks and networks with faster dynamics exhibit more rapid particle spread on the network, with little further improvement once a network has become well connected. As fragmented networks gradually become better connected, particle spread either steadily improves until the networks become well connected for slow-diffusing particles or plateaus for fast-diffusing particles. Mitochondrial fusion and fission have two types: end-to-end (lengthening and shortening tubes) and end-to-side (forming and removing three-way junctions). We compared model mitochondrial networks with both end-to-end and end-to-side fusion, which form branches, to nonbranching model networks that lack end-to-side fusion. To achieve the optimum (most rapid) spread that occurs on well-connected branching networks, nonbranching networks require much faster fusion and fission dynamics. Thus, the process of end-to-side fusion, which creates branches in mitochondrial networks, enables rapid spread of particles on the network with relatively slow fusion and fission dynamics. This work quantitatively describes how changing mitochondrial network dynamics affects protein spread and distinguishes the effect of end-to-end and end-to-side fusion and fission on spread efficiency.