I really don't know unless one analyzes the errors involved in the two approaches.And you really think that's more accurate than using the processors A/D converter to measure an analog voltage, such as from the bridge circuit?
What I do know is I can extend the resolution (number of bits) by counting for longer.
By counting over integral numbers of 50/60Hz AC mains cycles, one can reduce line frequency noise, in effect taking averages over a given period.