We have studied the electronic structure of the Ag(111)(root 3x root 3)R30 degrees-Sb surface alloy by angle-resolved photoemission. We find two hybrid surface bands, similar to the isostructural Ag(111)-Bi interface. The spin-orbit coupling induced spin splitting in momentum space, however, is strongly reduced from the Bi case. First-principles and model band calculations correctly reproduce this difference. The present results illustrate the complex interplay of atomic and structural contributions at the origin of the large spin separation in these systems.