I've been told by some old-timers (ropers and such) that mares have more "heart" than geldings. That a mare will try her heart out to please you and won't be as likely to quit if the going gets rough.
Geldings they say are more lazy and won't try as hard.
I've always preferred geldings. I've certainly owned more geldings than I have mares. And I don't worry about the "heart" as I am a trail rider and don't push my horses to their limits. I am out to have a fun ride, not do the Tevis Cup. But I could see if you were really pushing a horse that might be more important to a person. (Which makes me wonder....are their any statistics that suggest mares ARE better as performance horses?)
Right now though, I have the most awesome mare! I have only seen her "in season" about twice in 3 years. It's a non-issue and she is such a wonderful girl. Really, I consider her to be almost the same as a gelding.
She does have a lot more "go" than my current gelding. But I have also had geldings with "go" so that is a personality trait more than a gender trait.
She is also extremely loving an affectionate. If I am cleaning pens, she will just come and stand near me and doze with her head near my shoulder. I adore that. But again, I have had sweet geldings too.
I would not hesitate to own another mare IF I liked her. There have been a few mares that friends have owned that I would NOT own personally. I don't like mareish mares. But I think the good mares outweigh the bad. There are quite a few mares I would love to own.