More accurate? How so? You don't know the zero point in either case.
As the terminator between BCE and CE is an arbitrary date it is by definition a zero point. Using the birth of the Christ assumes a zero point that could be years off – and most likely is months off. There is also the problem of dates in the week following His birth. Assuming He was born on 25 December, what year would an event be in that occurs in the days immediately following His birth? Would it be BC – before He was born (no, that can’t be) or would it be AD (no, it can’t be that either because the date changes on the evening of December 31).