It's hard to get good comparisons, but over distance individual horses don't seem to out-perform human distance runners.
When humans used horses for rapid courier service they used relay tactics to take advantage of the horse's higher top speed, one horse might only run for an hour or two, before the rider reached another outpost and swapped a tired horse for a fresh one. In this way the relay could move something hundreds of miles in one calendar day. The Pony Express managed news of a US election from one coast to the other in just over a week.
If you can't use relays human and horse performance seem pretty similar, dozens of miles per day but not hundreds. The horse's top speed is higher, but it is rapidly exhausted, fast gaits like the canter are too exhausting to sustain for hours at a time.
