Ezri seems to be one of those characters people either love or hate. I understand both opinions. Personally, I liked Jadzia more but I liked Ezri too. She's different. I mean, look at the other main characters:
Sisko - Big bad bold bald guy. Eats Klingons for breakfast.
Kira - Tough-as-nails former terrorist. Downright scary when she's angry, tougher than most of the other characters on the show.
Bashir - genetically enhanced intelligence with superhuman reflexes and intelligence. Nice guy, but not to be trifled with.
O'Brien - average all around good guy, tougher than an Algorian mammoth.
Worf - it's Worf. 'Nuff said.
Jadzia - Klingon Party Girl, sweet and flirtatious but also quite capable of going toe-to-toe with most Klingons.
Garak - conniving, hardened, cold, awesome...and many other adjectives.
Ezri can't take on six Klingons at once or calculate the probability of winning the Dominion War in her head. She's not as conniving as Garak, she's not as tough as Kira or Jadzia, and she certainly couldn't hold her own in a fight against the legendary Dahar Master Koloth. She's cute, pretty, and feminine. But don't, under any circumstances, mistake that for weakness. Comparatively speaking, yes, she's far 'weaker' in on sense than the rest of the characters, but another Klingon Party Girl with a chip on her shoulder who's best friend is her Bat'leth would be absolutely pointless. The show had enough 'tough' characters. However, she can be tough when she needs to be as others have mentioned. Ezri's different. She's sweet, gentle, naive, cute, and a little bit neurotic. If you don't like her, that's your choice. But I think she's awesome. Although I admit I see why some find her annoying, and truthfully I didn't like her at first. But she grew on me.
I think it would have been better if she had been introduced BEFORE Jadzia died. That way it would have been a more meaningful character arc for her to get past her neuroses and fear and the shock of having Dax's memories. The way it happened she just got introduced as annoying and quirky. Which is fine, but it would have been more meaningful if introduced earlier.