Spin relaxation can be greatly enhanced in narrow channels of two-dimensional electron gas due to ballistic spin resonance, which is mediated by spin-orbit interaction for trajectories that bounce rapidly between channel walls. The channel orientation determines which momenta affect the relaxation process, so comparing relaxation for two orientations provides a direct determination of spin-orbit anisotropy. Electrical measurements of pure spin currents are shown to reveal an order of magnitude stronger relaxation for channels fabricated along the [110] crystal axis in a GaAs electron gas compared to [-110] channels, believed to result from interference between structural and bulk inversion asymmetries.