You are observing OPEN LOOP (no inverter communications) vs CLOSED LOOP (Communications between the battery and the inverter)
With Open-loop, the only 'view' into the battery that the inverter has is the voltage and current at its battery connections. Based on this voltage and current as well as whatever has been configured, the inverter decides all aspects of working with the battery. When to charge, when to go into the accumulation phase, when to go into float, when the battery is empty, etc. (Note that since other devices could be providing/using current and since there will always be voltage drop across the wires from the battery to the inverter, neither voltage or current is a precise indication of what is really going on with the battery.
With Closed-loop, the battery is in charge. It tells the inverter when to charge, when to go into the accumulation phase, when to go into float, when the battery is empty, etc. Since the battery (or the master battery) has a cell-level understanding of the system and is measuring both current and voltage at the battery, it has a much more accurate view of the state of the battery. Furthermore, since the BMS in the battery has an accurate view of the current, it can accurately keep track of state-of-charge and make decisions on SOC rather than Voltage.
Which is better? I have slowly moved from the open loop camp to the closed loop camp. (Will seems to be in the Open Loop camp) One reason for my change of position is that most vendors are now providing applications that hook to the inverter and can give a detailed view of what is going on in both the inverter(s) and the batteries. This is a powerful tool for configuring, debugging, and monitoring a system. Since I tend to help a lot of people build systems, it provides the added benefit of being able to remotely view the system when they call for help.
However, what really pushed me over the line to the closed-loop camp was learning about what is going on in the electronics within the system. With open-loop, the inverter can be charging or discharging at a high current when the BMS decides there is a problem, such as a cell overvoltage, and suddenly shut down. The Firmware in the inverter will detect the sudden change and follow suit by shutting down what it is doing. That all sounds fine but in that fraction of a second before the inverter shuts down, nasty things can be happening. The high current suddenly stops and inevitably that results in a voltage spike in the internal circuitry of the inverter. (Has anybody noticed the reports of 'DC Bus Overvoltage errors'..... this is what is going on.) Some inverters will be better at handling these events than others, but it can't be good on the circuitry of any of them. With closed-loop, the battery has the ability to tell the inverter to shut down in a more controlled manner. This coordinated event handling is much more controlled and easier on the electronics.