Anecdotally it seems to me that the "lazy, young, and failing at everything" stereotype is much more prevalent for men than women in popular media. On the other side the "young but really capable and never giving up" stereotype is much more common for women.
Of course inversions of these tropes can be found all over the place so to properly see if there's a skew you'd need to analyse a whole lot of media and see which is more frequent. I'm not about to embark on that project so the best I can give you is a description of how it feels to me.
In the end I don't think these sorts of stereotypes are too unbalanced, for every bad female stereotype you can find a bad male stereotype. I feel like the conversation shouldn't be about who has it worse and deserves compensation, it should be about how we decouple both good and bad stereotypes from gender or skin color or sexual orientation or what have you.
You need stereotypes to tell compelling stories, otherwise you'd have to explain every single character in-depth. This isn't a bad thing, but we need to be more careful about attaching stereotypes needlessly to real existing groups of humans.
If I were a script writer and it'd be up to me I'd probably just write the script with whichever stereotypes it needs, and then once the script is done flip some coins for the irrelevant character attributes such as gender or skin color or eye color. As far as I can tell those basically never matter for telling a story. Even in the case of it being historically inaccurate I wouldn't say it matters: you're already suspending your disbelief for a lot of stuff in the movies, the idea that e.g. a woman would be a commander in the first world war isn't a stretch big enough to break immersion.
I need to learn to write more coherently and start a blog I think.