With geldings (I've never ridden a stallion), you only have to win once. They fight for a while, but once you get their respect, they are consistent and easy to work with.
Mares, on the other hand, fight you all their lives. You can win a hundred times and they won't give up. And if you let them win at least once, they will disrespect you for a very, very long time, possibly forever.
Mares do have their advantages; when a mare loves you, she LOVES you. She'll give everything, plus more. You can't get that in a gelding.
In dressage, you need to be consistent. Stallions are consistent, but mares, like most females, are argumentative and love to second guess the rider. They have a mind of their own and show it.
I love mares. Mares have made me a better rider and forced me to adapt and not take things personally. They burn bright and go out, while geldings and stallion are kind of a dimmer, steady flame.