Age, general fitness, effort expended [rather than distance] seem to be the 3 main ingredients that determine rest required by horses and human runners.

It's no coincidence that generally, both move to longer distances as they get older [if suitable] and also take longer to regain peak fitness and need a longer recovery period. Apart from the fact owners are often looking to maximize return on investment as quickly as possible, 7 to 14 day breaks are far more common for young horses. They are able to 'do it again' more quickly than older horses without injury or risk to peak fitness ;-))