Let's see. I'll began with what I don't like to read or write about. In any case, I'm ok with that kind of stories, just not my cup of tea.
I don't like fights were one girl or more, or men, get severely hurt, like injuries including bones broken, big bruises and etc. I don't like blood, I also don't like punches to soft parts of the body, like breast of genitalia. Less with bare hands. I don't like hard scratching, less on soft parts. In conclussion, I don't like things that deals a aesthetical damage.
In terms of catfighting, I like amateur wrestling matches were both girls are equals in shape and size. I like boxing matches, but not brutal ones. I like spontaneous fights when somebody got quickly tamed by her opponent.
But I'm more interested in the sexfight section and also in body comparison, sexual comparison, etc. I like when the story gets psychological, with a girl getting defeated in a non-sexual or physical duel, but one in which another woman break her spirit only via dialogue or stealing her boyfriend or girlfriend.
I like topics like those where two girls fight for a man (or a girl) and they try to show him or her to be better. Despite I don't like physical damage at all, I like stories where mental or psychological cruelty reigns. Stories where a woman completely destroys the self-esteem of the other, well by sexually dominating her, well by conquering the man/woman in dispute in front of the loser.
I also like stories with close friends setting unsolved issues of the past and stories which involves siblings in a duel for a guy or simply to search out who's better.
I don't like stories with excesive fantasy, like cloak and dagger or futuristic stories, I don't like stories with extraterrestrial species, extrasensorial powers or superpowers.