“The Ashkenazi pronunciation is more correct. “
With accents, Ashkenazim very often mispronounce them. Pick up a Chumash and see where the accents are based on the Taamim. One on my Rebbis pointed out that misplacing the accent, like in the word viAhavTAH in k’riat shema, can change the meaning. Saying viaHAVtah changes the meaning and one may not be yotsai K”Sh (he was not sure though).
The “Sav” (Tav w/o a dagesh) comes from a different part of the mouth (palette) than the S,Z, and Sh sounds (teeth). See the Mishnat HaGR”A or Lishon Chayim. OTOH, I don’t think that it’s sound is a hard “T” like in modern Hebrew, but still the “T” sound is from the right part of the mouth.