The 800 V battery system is one of the solutions that allow for significantly increasing the charging power (compared to conventional 400 V), without increasing current values, which is important because of the thermal properties of the charging connector and cables.
In general, the increase of power, through the increase of voltage should also make the fast charging and general system more efficient.
Most recently, Hyundai Motor Group announced details of its Electric - Global Modular Platform (E-GMP), which will support 800 V natively.
The South Korean manufacturer has decided to develop the Integrated Charging Control Unit (ICCU), which offers DC fast charging at around 800 V (up to 350 kW), as well as at the more common 400 V level. Moreover, the ICCU is also an on-board charger (reportedly up to 11 kW) and can export up to 3.5 kW of AC power through the vehicle-to-load (V2L) function.
However, if the power electronics are designed for 800 V voltage, it might not work equally efficiently at lower voltage levels - or simply at 400 V DC chargers. This is why there is usually another step involved to boost the voltage.
In its presentation, Hyundai Motor Group shows two cases. The first is direct charging of the battery from the 800 V DC fast charging. The second one, on the right, is indirect charging from a 400 V DC fast charger, that involves power electronics (inverter) of the Integrated Drive Axle (IDA) to boost the voltage to the 800 V range:

We guess that the 800 V charging might be not only very quick (at ultra-high power levels of up to 350 kW), but also very efficient.
On the other hand, we would not be surprised if using the 50-150 kW chargers at 400 V would be a few percent less efficient. It might be actually slightly less efficient than in EVs natively designed for 400 V because of the additional step. This is something that we will look forward to testing.
Porsche Taycan
The first series-produced car that has an 800 V battery system is, of course, the Porsche Taycan, and it's also a versatile one, because it can operate on 400 V. However, if you use 400 V charger, the output is limited to around 50 kW (instead of up to 270 kW at 800 V charger). The higher levels, like 100-150 kW at 400 V can be unlocked by buying an additional package (DC to DC voltage boost converter).
In the U.S. this option cost $460:
On-Board 150 kW/400V DC Charger
"Optional On-Board DC Charger to increase maximum charging capacity when charging at public 400V direct current charging stations. By increasing the charging capacity to 150kW, the charging time is decreased."
We guess that Porsche was forced to limit the power level at 400 V because the 800 V power electronics would struggle to handle faster charging at roughly half of its nominal voltage.

See also
Gallery: Hyundai Electric-Global Modular Platform (E-GMP)
* all the 800 V and 400 V numbers are just nominal ranges, as the voltage changes significantly between the low state-of-charge and high state-of-charge.