We investigate the issue of end versus side branching of actin filaments by Arp2/3 complex, using a combination of analytic theory, polymerization assays, and quantitative modeling. The analytic theory shows that the effect of capping protein on the initial stages of actin polymerization in the presence of Arp2/3 complex depends strongly on whether new Arp2/3 complex-induced branches grow from the sides or ends of existing filaments. Motivated by these results, we measure and quantitatively model the kinetics of actin polymerization in the presence of activated Arp2/3 complex, for a range of concentrations of capping protein. Our model includes the most important types of events involving actin and actin-binding proteins, and can be adjusted to include end branching, side branching, or both. The side-branching model gives a better fit to the experimental data than the end-branching model. An end-plus-side model including both types of branching gives a moderate improvement in the quality of the fit. Another side-branching model, based on aging of subunits' capacity for branch formation, gives a significantly better fit than the end-plus-side model. We discuss implications for actin polymerization in cells.