The Question is should we trust the Batadz Eda Haredit Hashgacha? should we consider it on a higher level (and better) then Rabbanut?

The hashgacha of any Orthodox rabbi who proclaims that something is kosher is sufficient to accord it a kashrut status according to the halachic dictum that declares that one witness is sufficent regarding (most) prohibitions. If I am not mistaken, products with the hashgacha of the Edah Charedit also have the hashgacha of the local rabbanut - which is in itself sufficient unless you have well-based information (not rumours) that a particular mashgiach or rabbinate is untrustworthy.