What is the difference between $B\frac{C}{A}D$ and $BC\frac{E}{C}E?$

The $B\frac{C}{A}D$ system is more accurate, providing clearer context than $BC\frac{E}{C}E.$

The BCE$/$CE system adds $30$ years to the BC$/$AD system, so that you have to add $30$ years to the dates for accuracy.

Nothing. $BC\frac{E}{B}C$ simply removes the Christianized language of $B\frac{C}{A}D.$

The $BC\frac{E}{C}E$ system is more detailed, so that it provides more information than the BC$/$AD system.