The ability to judge speed is a fundamental aspect of visual motion processing. Speed judgments are generally assumed to depend on signals in motion-sensitive, directionally selective, neurons in areas such as V1 and MT. Speed comparisons might therefore be expected to be most accurate when they use information within a common set of directionally tuned neurons. However, there does not appear to be any published evidence on how well speeds can be compared for movements in different directions. We tested speed discrimination judgments between pairs of random-dot stimuli presented side-by-side in a series of four experiments (n = 65). Participants judged which appeared faster of a reference stimulus moving along the cardinal or oblique axis and a comparison stimulus moving either in the same direction or in a different direction. The bias (point of subjective equality) and sensitivity (Weber fraction) were estimated from individual psychometric functions fitted for each condition. There was considerable between-participants variability in psychophysical estimates across conditions. Nonetheless, participants generally made more acute comparisons between stimuli moving in the same direction than those moving in different directions, at least for conditions with an upwards reference (∼20% difference in Weber fractions). We also showed evidence for an oblique effect in speed discrimination when comparing stimuli moving in the same direction, and a bias whereby oblique motion tended to be perceived as moving faster than cardinal motion. These results demonstrate interactions between speed and direction processing, thus informing our understanding of how they are represented in the brain.