Frictional interfaces abound in natural and man-made systems, yet their dynamics are not well-understood. Recent extensive experimental data have revealed that velocity-strengthening friction, where the steady-state frictional resistance increases with sliding velocity over some range, is a generic feature of such interfaces. This physical behavior has very recently been linked to slow stick-slip motion. Here we elucidate the importance of velocity-strengthening friction by theoretically studying three variants of a realistic friction model, all featuring identical logarithmic velocity-weakening friction at small sliding velocities, but differ in their higher velocity behaviors. By quantifying energy partition (e.g. radiation and dissipation), the selection of interfacial rupture fronts and rupture arrest, we show that the presence or absence of strengthening significantly affects the global interfacial resistance and the energy release during frictional instabilities. Furthermore, we show that different forms of strengthening may result in events of similar magnitude, yet with dramatically different dissipation and radiation rates. This happens because the events are mediated by rupture fronts with vastly different propagation velocities, where stronger velocity-strengthening friction promotes slower rupture. These theoretical results may have significant implications on our understanding of frictional dynamics.