I didnt check the eso gears but from what I seen sch wouldnt go crit aswell and thats no-no-no-no-way. Ill focus to upgrade critpieces > rest and in case the old and new pieces both have no crit those will be right after. For me the rest only gets replaced if I am strongly in need of the additional HP or mind and for the HP I would even rather see what I can get crafted.
looks rather like a piety focus....