Reactions of molecules on metal surfaces are notoriously difficult to simulate accurately. Density functional theory can be utilized to generate a potential energy surface, but with presently available functionals, the results are not yet accurate enough. To provide benchmark barrier heights with a high-quality method, diffusion Monte Carlo (DMC) is applied to H2 + Al(110). Barrier heights have been computed for six geometries. Our present goal is twofold: first, to provide accurate barrier heights for the two lowest lying transition states of the system, and second, to assess whether density functionals are capable of describing the variation of barrier height with molecular orientation and impact site through a comparison with DMC barriers. To this end, barrier heights computed with selected functionals at the generalized gradient approximation (GGA) and meta-GGA levels are compared to the DMC results. The comparison shows that all selected functionals yield a rather accurate description of the variation of barrier heights with impact site and orientation, although their absolute values may not be accurate. RPBE-vdW-DF and BEEF-vdW were found to perform quite well even in terms of absolute numbers. Both functionals provided barrier heights for the energetically lowest lying transition state that are within 1 kcal/mol of the DMC value.