Jadzia Dax was a 100% useless character to the DS9 show. Both in terms of the writing for her, and the horrible acting by Farrell. Jadzia is easily and by far the very worst character on DS9.
As for the point that she was 'sometimes' used as a science officer: 100% of those lines are completely inter-changeable with O'Brien. Could have never had Jadzia on the show, gave O'Brien all those lines, and nothing would change. Just goes to emphasize very clearly how generic, poorly-written and useless of a character Jadzia was.
Characters are more than their jobs, especially on a show like DS9. I liked that since there wasn't much science to be done, they found other things to do with the character. They tapped into her history with Sisko for great effect in episodes like "In the Pale Moonlight" when she's serving as a Devil's Advocate. They remembered that her very old age had made her wise to what was good in life, so she had an appreciation for it, she seized every day, she had fun, she was bold, and she was smart. In that way here character was a meditation on life and death because both were so much a part of her history. They remembered that she had a history with some of the Klingon Empire's greatest warriors, so that, combined with here zest for life attracted her to Worf. She saw in him someone she could show how wonderful life could be and how to tap into his own heritage and move away from simply practicing Klingon rituals towards truly understanding the beauty and passion that made those rituals vibrant. She gave everyone a chance but stood up to those that wronged her or her friends.
In all of those ways, she wasn't quite like O'Brien. But yeah, if all you see in a character is who should say which system is down 47% then O'Brien or Nog would have sufficed.
I like Dax more than when the show was first-run, in part because she was underrated, attacked, and not taken seriously, but also because of what I've said above in this thread.