We study a new model for treating quantum dissipative systems, in which the bath is modeled as a collection of spins coupled to the system of interest. We develop a quasiclassical method to study this model, approximating the quantum Heisenberg equations by the classical ones, supplemented with stochastic initial conditions carefully chosen so that the results obtained from the classical equations are as close as possible to the quantum results. Using this method we compare the dynamics of such a spin-spin system with that of a spin-boson system, in which the bath is modeled as a collection of harmonic oscillators. We verify numerically that when the system-bath coupling is spread over many bath spins (the Brownian motion limit), the spin-spin model can be mapped on the spin-boson model (although with a temperature dependent spectral density). We also demonstrate that the two dissipative models are qualitatively very different in a non-Brownian motion regime.