Pinocchio - They are equally successful reporters, although the story focuses on the ML more.
I Hear Your Voice - FL becomes a competent lawyer.
Signal - not a romance but the FL is a good cop. She dates the ML who she had a crush on at some point.
Healer - I don’t know if I can say she’s his ‘equal’ because she doesn’t fight physically, but she seems to be competent in her job (also a reporter); hard to say if this fits the standard,but I didn’t find her weak either-it’s just that she has a trauma from childhood which recurs.
Dae Jang Geum -FL is the star of the show here. She’s a very competent doctor of sorts. ML has minimal role. There’s a little romance but it’s not the focus.