First Case: If you have owned your home only a short time, your taxable value may not be capped. In that case, your assessed value and your taxable value are equal. Consequently, if you appeal and get your assessed value lowered, your property taxes will be lower.
Second Case: Your taxable value may be capped, but it may be only slightly lower than your assessed value. In this case, if you appeal and get your assessed value lowered enough, then it would be less than your current taxable value. In such a case, your taxable value also will be reduced to equal the new assessed value. Your taxes will go down.