A model body-centered cubic (bcc) hydrogen solid is studied using density functional theory in the local spin density approximation (LSDA) and in the generalized gradient approximation (GGA). In GGA, the paramagnetic to antiferromagnetic phase transition occurs at a higher density, and is in much better agreement with previous variational quantum Monte Carlo (VQMC) calculations than LSDA. The metal-insulator transition in GGA is observed at a higher density and is also closer to the VQMC result than LSDA. In the limit of isolated hydrogen atoms, we find that in GGA the self-consistent electron density is greatly improved over LSDA due to a better cancellation of the electronic self-interaction.