We present a comparative study of two computer simulation methods to obtain static and dynamic properties of dilute polymer solutions. The first approach is a recently established hybrid algorithm based upon dissipative coupling between Molecular Dynamics and lattice Boltzmann (LB), while the second is standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions. Applying these methods to the same physical system (a single polymer chain in a good solvent in thermal equilibrium) allows us to draw a detailed and quantitative comparison in terms of both accuracy and efficiency. It is found that the static conformations of the LB model are distorted when the box length L is too small compared to the chain size. Furthermore, some dynamic properties of the LB model are subject to an L^ -1 finite size effect, while the BD model directly reproduces the asymptotic L \to \infty behavior. Apart from these finite size effects, it is also found that in order to obtain the correct dynamic properties for the LB simulations, it is crucial to properly thermalize all the kinetic modes. Only in this case, the results are in excellent agreement with each other, as expected. Moreover, Brownian Dynamics is found to be much more efficient than lattice Boltzmann as long as the degree of polymerization is not excessively large.