If faith in Jesus is not a barrier against sinning, in what way is it better than or different from O.T. animal sacrifice coupled with repentance?

**No Christian can claim that the fact they believe or have accepted Jesus as their personal saviour is a full-proof barrier against committing sin going forward.** Many discussions I have encountered on this forum take the view that Old Testament animal sacrifices and repentance were inneffectual and would not reduce the propensity to sin (they had become routine, repetitive, and "religious"). **If faith/belief in Jesus doesn’t stop one from sinning again, in what way is it better than or different from Old Testament animal sacrifice coupled with repentance?** **Many great men and women of the Old Testament times are recorded in scripture as having highly intimate and powerful relationships with God; so it can not be true that it was impossible to have a personal relationship with God under the belief system of those times.** If even Christians who have accepted Jesus as their personal saviour can fall into sin and repent; **is the advantage of the "new regime" only in the fact that we don't have to spend money buying sacrificial animals?**