There is no such thing as the best failure theory. The use of different failure criterion would would be appropriate for different materials. For example, the maximum principal stress/strain theory would be appropriate for brittle materials like cast iron or glass. On the other hand, the failure of ductile materials such as steel is best represented by the Tresca or Von-Mises criteria. The Mohr-Coulomb criterion would work well for material such as concrete, soil etc.