Should you expect male writers to be better at depicting male characters than female characters? What about women writers? Does every writer reveal his/her gender bias in prose?
This is a fascinating subject - read the discussion thread on the ASIMOV's Messageboard, where I put in a comment.
The gist of my argument in that thread is that any character must be placed in a believable context(setting) to make sense. Stereotypes become all the more glaring if they occur in a setting where you wouldn't expect to find them in the first place.
Of course a female character can be wimpy, helpless and neurotic - if you put her in a credible setting. For example in the upper middle class, a mental institution, or in serious trouble.
But if you place her in a spaceship crew going to Mars, she's a stereotype. (Helpless, neurotic persons can't become astronauts.)
Another common example is when characters in a historical context behave in a way that is too modern for the setting. I read one of Jean M. Auel's novel Stone Age romances (as a teenager, you learned to find the sexy parts), I reacted to this: one Stone Age character talks about being "depressed".
The term "depressed" implies a whole apparatus of knowledge, culture and ideas of the human psyche which plain couldn't exist 30-50,000 years ago. Prehistoric people didn't know what a "mind" was, and the earliest written stories (THE ILIAD, GILGAMESH etc.) suggest very different concept of the "soul".
Homer would not speak of "depression". With that word, the character reveals itself as out-of-place in the Stone Age setting, just as if she had said "Got some Prozac?"
When you write a character, remember: the more out-of-place your characters seem, the more your story resembles comedy. If it is comedy you want to write, that's fine...