Ultraviolet (UV) photodissociation experiments are carried out for Ar-n(HBr) clusters in which the HBr is adsorbed on the surface of the Ar-n, and also on isomers of these systems in which HBr is embedded within the rare-gas cluster. The mean size of the cluster distribution in the experiments is around (n) over bar=130. The kinetic energy distribution (KED) of the hydrogen atoms that left the clusters is measured. Molecular dynamics (MD) simulations of the photodissociation of the chemically similar clusters Ar-n(HCl) are used to provide a qualitative interpretation of the experimental results. The clusters with embedded HBr give a very cold H-atom KED. The clusters with the surface-adsorbed HBr give a KED with two peaks, one corresponding to very low energy H atoms and the other pertaining to high energies, of the order of 1.35 eV. The theoretical simulations show that already for n=54, there is a strong cage effect for the "embedded" molecule case, resulting in slow H atoms. The surface-adsorbed case is interpreted as due to two types of possible adsorption sites of HX on Ar-55: for a locally smooth adsorption site, the cage effect is relatively weak, and hot H atoms emerge. Sites where the HBr is adsorbed at a vacancy of Ar-n lead to "encapsulation" of the H atom produced, with a strong cage effect. A weak tail of H atoms with energies well above the HBr monomer excess energy is observed for the embedded case. Simulations support that this is due to a second photon absorption by recombined, but still vibrationally hot, HBr. The results throw light on the differences between the cage effect inside bulk structure and at surfaces.