I find the worst-written opposite-sex characters are those where the writer assumes the differences are greater than they are...
I just finished 'The Goblin Emperor' by Katherine Addison, and because I enjoyed it very much (sufficiently to read it twice back to back, in order to give me time to think about it deeply enough) I was trying to convince my wife to read it.
But in doing so I realized that the book lacks any well written female characters. All the primary drama concerns fairly believable relationships between men, and all the women are stereotypically dead, or superficial, or largely unimportant to the story, or are very broad stereotypes (or some combination of all of the above).
For example, the romantic love interest of the male protagonist, never arises above romantic love interest, and she is very stereotypically made simultaneously a hot nerd and a kick butt warrior woman. But in the context, given the quite maturity and dignity of the male protagonist and the distinct lack of swashbuckling action for her to "hold her own" in, her warrior woman shtick comes across as immature posturing, childish bravado, and affectation. Indeed, all the male character's with any amount of warrior bravado are sexist jerks, and at best it might come across in the female character as cute... but even that depends on a very patronizing take on what's supposed to be an intelligent 22 year old woman. It's not cute when an adult acts like a 12 year old, male or female.
And I realized that my wife probably wouldn't like it nearly as much, because among other flaws she'd find the female characters in this story shallow and even insulting. And ironically, this is in part because the author was trying to write gender positive characters, but instead just drew from a shallow pool of stereotypes - the progressive female scientist in a sexist conservative culture, the kick-butt warrior girl, the woman who wants a traditional man's job, etc. This despite, or maybe even because, the story was written by a woman.
So I reject the notion that the gender of the writer determines whether they can write strong characters of a particular sex. I gave up on 'The Dresden Files' because in part I found the author's male characters thinly drawn and borderline insulting. Shallow characters are seldom enough to ruin the story entirely - I still enjoy some Heinlein's despite the fact that he only ever has about 3 characters and they are all dumb - but it is a consideration.
I agree with you that vast expanses of human experience are experienced in common, and I generally disapprove of theories that say someone's experiences are so unique that someone that doesn't share their race or gender shouldn't right about them.