I've noticed a trend that in may series where there is any sort of comparable skill the author tends to favour one gender over the other. Generally if it's female leaning there's almost zero compitent males; and in male leaning the women are always two or three steps behined. I particularly noticed this very heavy in battle manga.
So I'm looking for male and female charcters who stack up to each other pretty equally in anything really, fighting, sports, brains, childrens' card games, handjobs or etc. This has to be more than just one or two excpetions. Only titles that come to mind right now are Tenjou Tenge (maybe Air Gear, but I never finished it), and Aiki-S. Even though this is a pretty broad idea I don't have any genre restriction.
Maybe Hoshi no Samidare - There's one overpowered character, but it never comes to a gender being favoured over another one, at least not in skills
Sayonara Football might be an interesting one, as it explores exactly the struggle of a growing girl who realizes she can't keep up physically with her male friends, but who's the best one in terms of pure skills
Soul Eater has quite the powerful main characters, be them girls or boys. This one in particular tends to cater to young male readers, given the consistent amount of ecchi.
Beauty Pop might fit. The girl is better than the guy, but the guy is not an incompetent nincompoop. He's the most talented male, she just happens to be more talented than him. Also, in their youth, the guy's dad was never able to beat the girl's dad. So in a way it's less of the girl being better because she happens to be the main character and more her dad was better than the other guy's dad and now they inherited that feud.
Chihayafuru, perhaps? It is about card games as you mentioned above (karuta), but has a feel of a sports manga. I never noticed a gender imbalance, and both genders compete against each other. The protagonist is female.