In its first absorption continuum, a variety of channels are available to the permanent dissociation of matrix-isolated H2S, the two main ones being cage exit to yield SH + H and the cage-induced bimolecular reaction SH + H --> S + H-2. Laser-induced fluorescence (LIF) from SH(A-->X) and S(S-1-->D-1) is used to probe each of these channels. LIF of S atoms is a site-specific probe that can distinguish among interstitial and substitutional sites and sites at which the S and Hz products are crowded together. In addition to substitutionally trapped S atoms, interstitial trapping is observed. The latter implies cage exit of S(D-1). In the crowded sites, the LIF signal from S is stable, implying that there is an activation barrier to reaction of S(D-1) with Hz. In Kr, the SH:S branching ratio increases monotonically from 0.7 to 3 for excess energies between 1 and 2.5 eV. The quantum yield of the S channel is nearly independent of photodissociation energy, while the SH channel yield increases monotonically with excess energy. A statistical model, based on cones of reactivity, is used to rationalize the branching of the cage-induced reaction H + SH to yield H2S or S + Hz. A statistical theory for sudden cage exit, which incorporates barrier height distributions due to zero-point and thermal fluctuations of the lattice, is presented and used to characterize the nature of cage exit dynamics. At large excess energies sudden exit becomes the dominant channel. However, it is clear that near threshold the fragment exits over a deformed barrier, after extensive energy transfer to the lattice. The treatment is successful in predicting known energy, temperature, isotope, and mass asymmetry effects controlling sudden photodissociation dynamics of hydrides.