At present, many similar but disparate input-output (I-O) stability criteria exist. Without means for comparison, it is unclear which result is best used in any given application. This paper proposes a means for comparison between I-O stability results involving norms and inner products of inputs and outputs. The extended conic sector theorem provides a framework for determining which results are least conservative and most broadly applicable. In so-doing, numerous existing stability results are unified and revealed as more powerful than previously thought.