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.
Since you're implying there is no difference between science and engineering, you could take O'Brien's lines and give them to Jadzia. Better yet no O'Brien at all would mean no Keiko and Molly, who were far more useless than anyone, let alone Jadzia. You could take Worf's lines and give them to O'Brien since Miles has more experience as a tactical officer then Worf. Contributions are best measured by what the character actually did, not just said. She was effectively used as a science officer until the war took over as the primary arc. Even then she commanded the Defiant in Sisko's absence, along with being his closest friend and confidant.