Quantum-dot cellular automata (QCA) are an attractive emerging technology suitable for the development of ultra-dense low-power high-performance digital circuits. Efficient solutions have recently been proposed for several arithmetic circuits, such as adders, multipliers, and comparators. Nevertheless, since the design of digital circuits in QCA still poses several challenges, novel implementation strategies and methodologies are highly desirable. This paper proposes a new design approach oriented to the implementation of binary comparators in QCA. New formulations of basic logic equations required to perform the comparison function are proposed. The new strategy has been exploited in the design of two different comparator architectures and for several operands word lengths. With respect to existing counterparts, the comparators proposed here exhibit significantly higher speed and reduced overall area.