If you're asking preferences to mares, stallions or geldings, I have one of each currently (horses, not minis) and they are all incredibly different.
The mare: She has a standard of kindness. She will try her heart out for you if you are patient in your explanation. She responds very well to positive words and pats. She does not tolerate arrogance. Definitely a leader in her own.
The stallion: Sire to the afore-mentioned mare. I'd created him so we have a 12-year history. He much prefers that he doesn't have to make decisions in his life, he'd rather have a clear leader that tells him where he needs to be and what he needs to do. He is not brave although is the "herd protector" when challenged. He loves consistency. He does not respond to force, he despises a whip but respects spurs. He is very kind and gentle and also loves to be fussed over. He will tolerate more than the mare.
The gelding: He's related to the mare through the dam's site. He's a big goofy ball of fun. My most trusted partner. Little phases him. Has far more tolerance to stupidity. Would rather eat cookies than be fussed over, but still enjoys attention and interaction. Much better at making decisions when needed.