The difference from the 2001 to 2001M should not be that large. According to the XDEVs article the main point is with the AC part that also support average responding AC mode.
From the reports here in the forum it is a relatively noisy meter. Form the ADC design it is a bit similar to the HP3456 and may have comparable performance. The 20 V range can be nice if one needs it, but for directly meassuring a reference a 10(12) V range would likely be more suitable.
A slightly odd point in the K2001 is that the ADC itself uses a separate (low noise, but not very stable) reference and there are extra 7 V reference measurements from time to time. I don't know the details - it could be a old style cycle like in the older K192/3 with a reference measurment in every cycle, but clould also be more complex. The extra reference reading adds noise (at least from spending some time there), but can in real time correct ADC gain drift. The other point is that the 20 V range has a divider (amplifier with gain -0.5) in the signal path that is not corrected with the reference reading. The HW side seems to support a 10 V range (likely used for the Ohms part), but AFAIK it is not normally available for DCV
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For testing a reference the ideal case is measuring the difference to a 2nd, stable reference. A direct reading would have the DMMs reference as a limiting factor.
The way the K2001 input is made I would expect extra noise, as there is only a somewhat limited AZ mode for the 20 V range. It may look different from the noise hump seen in many other Keithley meters.