Instead of digits, look at counts. The 34401A is 1,200,000 counts, the Brymen is 500,000 counts. So the 34401A only has 2.4X the counts.
The Brymen just happens to have its maximum resolution (in counts) right at 5 volts, but unless it overranges, as soon as you go to 5.00001 volts you lose a digit.
I have no idea what you are doing, but unless you want to look at noise, this whole thing doesn't make sense. At exactly 5 volts the Brymen as a resolution of 2PPM, but a rated accuracy of more than 100X worse--200ppm + some counts. Even on the 34401A, the last digit is very questionable.