Wow... a lot going on in this thread.
Why do I like Ezri?
She's brave. Despite being confused (and who wouldn't be, by what happened to her?) and physically small, she takes on problems whether psychological, political, or physical. And she's resourceful enough to succeed.
She cares about people - her friends, her family.
She's a Trill, and her story is about being a Trill. A new race, focused on in DS9, that never got developed enough.
She's beautiful, in a way that appeals very much to me. (Whereas Jadzia or Seven are beautiful in a way that I admire, rather than makes me think "if she were real I'd be in love").
On the other hand - she was held back by a couple of problems.
I don't think a counselor is a great concept for a Trek character. I don't think it worked for Troi or Ezri.
She was introduced way too late - should have come in about halfway through the show.
Jadzia
Not my favorite character, although I don't really agree with the people who don't like her at all, either.
I hated how every story about her, even before Worf, was all about Curzon and the Klingons. It wasn't about Trill society, and it wasn't about having lived nine lives before meeting all sorts of interesting alien races... it was about one past life, and Klingons. And more Klingons. And more boring, stereotypical Klingons.
Her flirting with Quark was always harmless. She should have been, with her ancient perspective, a little more careful with Bashir. That doesn't mean he wasn't an idiot for keeping his hopes up, and it doesn't mean she was constantly manipulative - just that she could have avoided sending mixed signals, which she definitely did at times. If she was supposed to be genuinely confused, we never saw it. Bashir at the start of the show was far more immature than Ezri was when she joined the show.
(By the time Worf called Bashir a boy, I think Bashir was far more emotionally mature than Worf, although their respective issues were quite different.)
Bias in contemporary culture
I find it odd that to counter claims that there are bad portrayals of men in contemporary popular culture, people are pointing to bad portrayals of women. Relevance, your Honour, doesn't speak to the question...
One thing I like about Trek is that it generally has positive portrayals of people, including on DS9 where the main cast remain admirable, positive people - men and women - despite having flaws and despite dealing with some pretty murky ethical dilemmas.
It's interesting to debate and criticize where Trek fell short, but on the whole this is something where Trek is head and shoulders above the vast majority of TV.