The HP34401 can do faster than 1 PLC, but this comes with a reduced resolution and of cause no more 50/60Hz suppression.
For the speed one also has to look at the auto zero setting: with AZ active the total conversion takes twice the time (for a input reading and a zero rading). With some other old meters (e.g. Keithley 19x) the AZ mode may take 3 actual conversion and thus 3 x20 ms (for 50 Hz 1 PLC). Chances are one would want the non AZ mode for the fast readings.
The performance in the 100 mV range may not be that good (drift and LF noise) in non AZ mode.
The Sigilent and Rigol meters based on a SD ADC chip tend to not suffer much from non using the AZ mode. For the specific task of fast reading and calculating RMS they can be a good choice (even the SDM3055). The weak point is more with long term drift and some software issues that to a large part seem to be solved for the Sigilent side.
The 34410 is internally quite different from the 34401, it is more like the modern 34461 with an old style display.