In many Iberian breeds (particularly in Latin countries) it's not the custom to geld a stallion unless there is a serious conformational or tempermental flaw.
Stallions are for riding; mares are for breeding.
In the U.S. We tend to follow the British/Northern European practice of gelding all but the best stallions (those which will be used for breeding).
Gelding does NOT
remove "male" tendencies (aggression, mare herding, mounting, etc.). These "stallion" behaviors are instinctive. You can prove this by watching suckling colts play and comparing their play to suckling fillies. Gelding removes the fuel that "amps up" these behaviors.
Gelding will usually result in some physical differences at maturity. These changes generally do not negatively impact the utility of the horse.