van der Waals functionals have recently been applied to obtain a potential energy surface to describe the dissociation of H2 on Ru(0001), where an improvement was found for computed reaction probabilities compared to experiment, which could not be achieved with the use of other exchange-correlation functionals. It is, however, not yet clear to what extent van der Waals functionals give a better description of other molecule-metal surface systems. In this study, the optPBE-vdW-DF functional is compared to the SRP48 functional, which was originally fitted to describe the dissociation of H2 on Cu(111), in terms of the resulting potential energy surfaces and results of quasi-classical dynamics calculations and their agreement with experiment for different H2-metal surface systems. It is found that overall the optPBE-vdW-DF functional yields potential energy surfaces that are very similar to potential energy surfaces computed with the SRP48 functional. In dynamics calculations the optPBE-vdW-DF functional gives a slightly better description of molecular beam experiments. Also a different dependence of reaction on the rotational quantum number J is found, which is in better agreement with experimental data for H2 dissociation on Cu(111). The vibrational efficacy is found to be relatively insensitive to which of the two functionals is chosen.