One thing that hasn't been mentioned is calibration, if you are so inclined. I have both the HP 3456A and the Fluke 8506A. The 3456A is
quite simple to calibrate and involves turning a few pots (accessible from a removable section of the front panel). The 8506A, however,
was a nightmare, at least for me. You can do a "hardware" calibration, which involves turning pots, or a "software" calibration which stores
zeros and gains into nonvolatile memory. The manual is clear as mud on the entire subject. I ended up trying the software cal, but the
linearity seemed to suffer and was much worse than the 3456A. So I ended up doing the hardware cal. This restored the linearity of the
8506A to 3456A levels, and why not - after all, the hardware cal has you adjust a whole bunch of intermediate points in the A/D ladder.
Anyway, I think I ended up doing both the hardware and software cals, maybe that was a mistake. As I said, the manual was very confusing
in my opinion.
Both DMMs are nice units. But for serviceability, I like the HP better than the Fluke with its series of self-contained modules (for which you
need extenders).