Yes, at any particular 800V capable charging station, an 800V vehicle will likely receive more power than a 400V vehicle, provided both vehicles are capable of receiving the max current of the charger.
It's actually even more complicated than that though. Here is the operational curves from the ABB Terra spec sheet (not quite the one you showed, but in the same family):
View attachment 845391
So any given charger is going to have 3 separate limits: the voltage (X axis), current (Y axis) and power, which is the reason the upper right corner is cut off on these curves.
Unfortunately a lot of these details are going to be lost on the average consumer that pulls up to a charging station labeled "350kW" and when they plug in their vehicle they are only pulling in 200kW.
Anecdote: I was at an ElectrifyAmerica station, having difficulty with the 150kW station that we were plugged into (it was bouncing between delivering about 50kW and dropping down to almost 0). The adjacent 150kW stall opened up (but was showing unavailable on the app, and we needed to initiate with the app to get free charging), and then one of the two 350kW stalls opened up. We went to move the car to the 350 when a Bolt drives up and starts pulling into the now open 350 spot. I try to explain the situation and ask them if they can use the 150kW station (that showed unavailable for us, but was working fine). They pull into that spot, and as my wife starts to move the car over to the 350, they grab one of the cables from the 350 (EA stations have 2 cables, not to accommodate dual charging, but rather to provide access to cars with different charge port locations) that we were going to use and plugged in.
I told them that that was the station we were going to use, but they insisted that we could both charge because there were too cables. I told him it doesn't work like that (that only one of the cables could be used at any given time), and that their car could only charge at 50kW anyway, so they should just use the 150kW station they were parked at (and now blocking! -- there had been a 3 car queue when we arrived at this busy station). They would have none of this, however, explaining that they had a new, special Bolt that charged at "259" (this was the range, not the power!) and that I didn't know anything about Bolts (yeah, well my wife had owned one just prior!). It actually got a bit heated, and as that was happening, fortunately the other 350 opened up, so my wife pulled into that spot and we got a nice fast charge, but meanwhile, a Polestar pulls into the vacant 350 spot that the Bolt owner was trying to use. He plugs in and starts charging and I walk away from the Bolt people and let them figure it out themselves.
Sure enough the guy eventually walks over with his tail between his legs and admits that yes, two cars can't charge from the same EA station and yes, I was right about the car only pulling 50kW.
And this was a relatively simple case. Now we're throwing sites with different power stations, variable battery conditions, unreliable hardware, and overly simple nameplate specs into the mix and it's going to be a huge mess out there.