We use scanning tunneling microscopy and x-ray spectroscopy to characterize the atomic and electronic structure of boron-doped and nitrogen-doped graphene created by chemical vapor deposition on copper substrates. Microscopic measurements show that boron, like nitrogen, incorporates into the carbon lattice primarily in the graphitic form and contributes ~0.5 carriers into the graphene sheet per dopant. Density functional theory calculations indicate that boron dopants interact strongly with the underlying substrate while nitrogen dopants do not. The local bonding differences between graphitic boron and nitrogen dopants lead to large scale differences in dopant distribution. The distribution of dopants is observed to be completely random in the case of boron, while nitrogen displays strong sublattice clustering. Structurally, nitrogen-doped graphene is relatively defect-free while boron-doped graphene films show a large number of Stone-Wales defects. These defects create local electronic resonances and cause electronic scattering, but do not electronically dope the graphene film.