Its down to the individual horse
As the old saying goes you ask a mare, tell a gelding and suggest with a stallion.
However I have seen moody, bad tempered geldings and calm willing mares and if trained correctly and treated with care and respect, stallions also make very good horses. Many top riders agree on a good day a good mare is unbeatable and are often more courageous than geldings. Although generally speaking geldings are the most laid back and amiable and mares can prone to being mareish.
I think the most important thing is finding a suitable horse for what you want to do whether that be a mare or a gelding. Bare in mind that all horses have feelings regardless of sex if you are going to get tough with them, geldings are no different to mares in that respect. Also horses have off days just like people and may not feel like doing something hence not performing to your standards when being schooled.