Speed would be one. A horse can't maintain a fast pace for very long. A human on a bike can go much further than a horse can run in one day. That said, presumably the lack of appropriate roads would nullify that advantage.
This does not show that a man can go "further". It's about who ends first.
And even at that, the race started at 1980, but the first time a man on foot won the race was in 2004.
One "man on foot" win in 24 races and that man being a marathon runner, does not bode well with the idea that man in general can outrun horses for long distances.
It is rare for humans to actually be physically capable of it these days, but chasing animals until they collapse from exhaustion is something hairless sweating bipedal are built for. The very best horses could still do it, but attempting persistence hunting on horseback with most horses would probably injure the horse.
Of course horses have been selectively bread for endurance for thousands of years so arguably their achievements are human achievements, but that's beside the point. ;)
