I loke them when done well. Like in old horror movies, where they start off as just an average girl, go through some real fucking shit, come out worse for the wear, but tough as nails. That kinda thing.
Also, 90's "tough, but still sexy" types are nice, when not done solely for the sex appeal side of things. They have to be well written too.
Female super heroes are great, as long as they don't exist solely to call constant attention to the fact that they're female.
The modern version usually boils down to 2 varieties:
Perfect person who makes zero mistakes and can moraculously do everything perfectly, in stressful situations, with limited time, in the first try, even though they've never tried before. Usually just vaguely sexist, where they're shown being better than everyone (especially men) but at least connect with other women and minorities.
Or the "deeply flawed, but well meaning" type, who is basically the same as the other variety, but usually more overtly sexist (mocking men constantly for no reason). And usually do fuck up, but are still amazing at everything to the point that their fuck ups are obviously just there for conflict and make their.stories.drag more than anything.
Those are just cringe, and will keep me away from the media they're in. No matter what it is.
That said, I also try to avoid male characters like those as well. I usually hate it when there's some perfect, smug dude who's perfect and everyone is constantly amazed by his perfection and badassery. It's just bad writing.
That's why I hate Superman (in the wrong hands) and the Bourne movies.