We present a comparative density functional study of the adsorption of hydrogen on bilayer graphene. Six different exchange-correlation functionals are employed to explore the possible configurations of hydrogen ad- sorption at 50% coverage. Using the four variants of the non-local van derWaals density functional, we identify three distinct competing configurations that retain the coupled bilayer structure at 0 K. One of the configurations undergoes a spontaneous transformation from hexagonal to tetrahedral structure, under hydrogenation, with heat of formation ranging between -0.03 eV (vdW-DF) and -0.37 eV (vdW-DFC09x). This configuration has a finite band gap of around 3 eV, whereas all other competing configurations are either semi-metallic or metallic. We also find two unique low-energy competing configurations of decoupled bilayer graphene, and therefore suggest the possibility of graphene exfoliation by hydrogen intercalation.