Counter-rotating turbomachines have the potential to be high efficiency, high power density devices. Comparisons between conventional and counter-rotating turbomachines in the literature make multiple and often contradicting conclusions about their relative performance. By adopting appropriate non-dimensional parameters, based on relative blade speed, the design space of conventional machines can be extended to include those with counter-rotation. This allows engineers familiar with conventional turbomachinery to transfer their experience to counter-rotating machines. By matching appropriate non-dimensional parameters, the loss mechanisms directly affected by counter-rotation can be determined. A series of computational studies are performed to investigate the relative performance of conventional and counter-rotating turbines (CRTs) with the same non-dimensional design parameters. Each study targets a specific loss source, highlighting which phenomena are directly due to counter-rotation and which are solely due to blade design. The studies range from two-dimensional blade sections to three-dimensional finite radius stages. It is shown that, at hub-to-tip ratios (HTRs) approaching unity, with matched non-dimensional design parameters, the stage efficiency and work output are identical for both types of machines. However, a CRT in the study is shown to have an efficiency advantage over a conventional machine of up to 0.35 percentage points for a HTR of 0.65. This is due to differences in absolute velocity producing different spanwise blade designs.