Inverter technology has caught on in the North American heat pump market, with most major HVAC manufacturers offering the feature not only in mini-splits, but in traditional split system configurations as well. While the benefits of inverter modulation over traditional compressor staging (improved part load efficiency and more even run performance) and compressor unloader modulation (which is less effective at boosting part load efficiencies) are fairly clear, what is not clear is what is necessary to gain that efficiency.
Some inverter heat pumps (Bosch Thermotechnology units to be precise) use traditional Y and O/B inputs from the thermostat, relying on sensed discharge and suction parameters to modulate the compressor to the appropriate level. A few others (Nortek-made units, it seems) accept inputs from either a single-stage or a two-stage thermostat, and presumably again rely on internal sensors (in conjunction with staging inputs) to determine the appropriate degree of compressor modulation. This is what I am calling "self-modulation", as the outdoor unit controller is autonomously or near-autonomously determining the compressor turndown instead of relying on the thermostat to do it for them.
However, most inverter heat pumps, it seems, rely on the thermostat to tell them how much compression is necessary in the system, and those that do nearly universally use a proprietary "fieldbus" (often using a RS-485 physical layer, run over 3 or 4 wires) to allow the thermostat to tell the outdoor unit how much grunt to give, a system I call "command modulation" as the outdoor unit is being told by the thermostat how much to modulate. (P.S. if you're wondering about mini-splits at this point, I have not seen a mini-split that is not command-modulated, but they pose...other system integration hurdles, so they are out of scope for this question.)
What are the significant/categorical performance or efficiency advantages of the command-modulated approach over the self-modulated approach to an inverter split system heat pump? For the purposes of this question, you can assume that the system has been sized correctly for the house using Manuals J and S with 99% heating and 1% cooling outdoor design temperatures in a mixed (Climate Zone 4 or 5) climate, and is driving an ECM air handler feeding ductwork designed as per Manual D and installed to plan entirely within the conditioned space.