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.

Akira and Mother Sarah for action manga.

Nodame Cantabile - the characters are music students and there are various competitions and performances and so on.

Hachimitsu to Clover would fit too (characters are art/architecture students) but there's no emphasis on competition.

Futatsu no Spica -- They strive to be good astronomy students, and I don't recall there being any gap by gender, provided my memory isn't failing me.

Black Lagoon, maybe. But I didn't read far enough to be certain.

And possibly Zettai Karen Children.

I'd say the survival skills are pretty evenly distributed among the genders in 7 Seeds. There's about the same amount of losers and geniuses in both sexes.

Quote from calstine

Black Lagoon, maybe. But I didn't read far enough to be certain.

I was going to use that as an example but only one, maybe two, male characters that I can think of come even close to Revy or any of the other super human women.

Butter!!! - Ballroom club, they're pretty much equal in their struggles and improvements.

Noragami - Gods and weapons are all quite strong regardless of gender

Fullmetal Alchemist - We get a wide range of characters for both genders

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.

My current top 3:
Fullmetal Alchemist
Pandora Hearts
3-gatsu no Lion

Bump

Hitsugi no Chaika Akari and Tooru appear to fight on equal ground.

Kekkaishi Yoshimori and Tokine also fight on equally although occasionally one will surpass the other.

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.

Psyren
https://www.mangaupdates.com/series.html?id=19081
Amamiya and ageha are equals, one can even debate that she's stronger than him. They also both have a romance thing going on, and yet she remains his equal throughout the entire manga.