Horses seem to be a much more common sight in so-called "developed" (or rather "heavily mechanized") countries than donkeys are while the latter seem to be still quite popular in many "developing" countries†. The accepted reason for this seems to be that donkeys were/are commonly used as beasts of burden/work animals, but of course are likely replaced by mechanization once countries become "developed".
Work/draft horses seem to have followed a similar pattern of decline; However, horses in general are still quite popular in developed countries and even draft horses enjoy some niche roles despite the fact that they don't really do "work" in the way it was meant before: Many are used for ceremonial purposes, animal fancy, sport, etc.
Therefore, if horses can "evolve" into having roles outside of "work", why hasn't the same thing happened with donkeys?‡ — Where are the fancy donkey breeds? Donkey dressage contests? Donkeys dressed up in foofy costumes pulling tourists around?
† This is of course a gross generalization, as e.g. China and Mexico could hardly be called "under-developed" yet they both have loads of donkeys.
‡ In fact, there are some e.g. donkey breeding contests, etc. but they are extremely uncommon in comparison to the amount of analogous events for horses.