We compare and contrast the wide Feshbach resonances and the corresponding weakly bound states in the lowest scattering channels of ultracold Li-6 and Li-7. We use high-precision measurements of binding energies and scattering properties to determine interaction potentials that incorporate non-Born-Oppenheimer terms to account for the failure of mass scaling between Li-6 and Li-7. Correction terms are needed for both the singlet and the triplet potential curves. The universal formula relating binding energy to scattering length is not accurate for either system. The Li-6 resonance is open-channel-dominated and the van der Waals formula of Gao [J. Phys. B 37, 4273 (2004)] gives accurate results for the binding energies across much of the resonance width. The Li-7 resonance, by contrast, is weakly closed-channel-dominated and a coupled-channel treatment of the binding energies is required. Plotting the binding energies in universal van der Waals form helps illustrate subtle differences between the experimental results and different theoretical forms near the resonance pole.