Yes,
Andy, BMCC has ISO 800 as its lowest.
And that's why you have to use ND filter more often than not on BMCC.
And this is basically how I would do the test ideally: clean lens on 50D and ND8 on BMCC.
I didn't get your part on pulling shadows down. Usually to increase the visible DR (and to approach the iconic filmic look) I push the shadows up. I guess everybody else does, no? )
And the noise (if pushed in ACR to Gamma 2.0) looks like this: BMCC is cleaner, 50D has surfacing the rectangular pattern. But both manageable to some extent, I agree.

But I do,
I do second you -- looking at this difference, I don't see a 5-year gap between these cameras. Nor a $1500 gap )