I ran CMBIs for a while and really liked them. I have no reason to believe they sound any different (worse) than CMCs and think they're ideal when running into unbalanced inputs. CMBI > Sony M10 is compact setup that will rival anything.
What I didn't like about the CMBIs was running them with phantom powered recorders/preamps. I was always nervous about accidentally turning on the phantom power and potentially damaging the CMBIs. Not sure if that would actually happen, but it was on my mind. The CMBIs can be powered by the internal 6v battery or via external power (wiring diagrams are found in the manual) and a PFA could provide 7-13 V required, allowing you to run these easily with a balanced, phantom powered input.
Per the manual, you can't use the KC, RC, SKC, CUT 1, or BLM 03 C components with CMBIs. However, the CMBI body has a -15 dB pad built in if required.
Here a
link to a few recordings I made with the CMBI's... not sure if I have anything convenient that isn't an sbd mixdown.