We investigate experimentally and theoretically effects of the inter-core propagation mismatch on nonlinear switching in dual-core high-index-contrast soft-glass optical fibers. Incident femtosecond pulses of various energy are fed into a single (“straight”) core, to identify transitions between different dynamical regimes, viz., inter-core oscillations, self-trapping in the cross core, and retaining the pulse in the straight core. The transfer between channels, which has solitonic character, is controlled by the pulse’s energy. A model based on the system of coupled nonlinear Schrödinger equations reveals the effect of the mismatch parameter and pulse duration on the diagram of the various energy dependent dynamical regimes. Optimal values of the mismatch and pulse width, which ensure stable performance of the nonlinear switching, are identified. The theoretical predictions are in agreement with experimental findings.