A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1) symmetry which is known from previous studies to mix up antiferromagnetic order parameter with that of the p -type nematic, we find an emergent U(1) symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g., the bosonic t-J model) is also discussed. © 2006 The American Physical Society.