The electronic excitation induced by ultrashort laser pulses and the subsequent photodissociation dynamics of molecular fluorine in an argon matrix are studied. The interactions of photofragments and host atoms are modeled using a diatomics-in - molecule Hamiltonian. Two types of methods are compared: (1) quantum-classical simulations where the nuclei are treated classically, with surface-hopping algorithms to describe either radiative or nonradiative transitions between different electronic states, and (2) fully quantum-mechanical simulations, but for a model system of reduced dimensionality, in which the two most essential degrees of freedom are considered. Some of the main results follow: (1) The sequential energy transfer events from the photoexcited F2 into the lattice modes are such that the "reduced dimensionality" model is valid for the first 200 fs. This, in turn, allows us to use the quantum results to investigate the details of the excitation process with short laser pulses. Thus, it also serves as a reference for the quantum-classical "surface hopping" model of the excitation process. Moreover, it supports the validity of a laser pulse control strategy developed on the basis of the "reduced dimensionality" model. (2) In both the quantum and quantum-classical simulations, the separation of the F atoms following photodissociation does not exceed 20 bohr. The cage exit mechanisms appear qualitatively similar in the two sets of simulations, but quantum effects are quantitatively important. (3) Nonlinear effects are important in determining the photoexcitation yield. In summary, this paper demonstrates that quantum-classical simulations combined with reduced dimensionality quantum calculations can be a powerful approach to the analysis and control of the dynamics of complex systems.