So it's due to both voltage and current, just not clear to what degree each plays a part. There must also be something related to software limitations in output too because cars with different pack power outputs get similar performance - the 85D, 90D, and 100D.
Performance is limited by whatever the weakest link in the chain is. The Performance cars are built to minimize the limits of every component and get as much power from the pack to the wheels as possible on launch. Limits could be wiring, the inverter, the motor, or the peak output capacity of the pack. With the non-performance 85D, 90D, and 100D, the key limit appears to be what the motors can handle. The rear motor is smaller than the rear motor on the Performance cars. I believe the inverter on all the cars is the same (or was before the latest change). The wiring is also probably the same on all cars.
On the small pack cars, the pack can't produce as much peak power as the larger packs could and this was the limiting factor. Take an old 70D or 75D and put a pack from a 90D in it, then change the firmware so it knows there is a larger pack, and you should have identical performance to a 90D.
How much current or how much voltage doesn't make much difference (within practical limits). The old 90D pack could produce 311 KW peak power (according to Wikipedia). That's 777.5 A at 400V. 888.57 A at 350V is also 311 KW. As far as the inverter is concerned, it makes no difference, the inverter will convert that to the AC needs of the motor.
Putting all the cells in parallel is impractical, that would result in a 4V battery pack with 77,750 A. That kind of current would be very hard on the wiring as power loss is I^2*R. The resistance of copper cabling is very low, but with that kind of current squared, the losses in the cabling will be huge.
Wiring all the cells in series to make a 28 KV battery pack with 10.9 A is also impractical. The higher the voltage the further it can jump from one point to another. In dry air 24 KV can jump about a 1 inch gap. The odds you're going to get unwanted arcing in the drive system is way too high.
But in the range of say 300-800V, you can make an inverter to take in any voltage in that range and the currents will be reasonable unless you have a massive battery pack. The semi will probably have an 800V pack to keep the currents down around where they are in the cars or maybe 2X (depending on how big the pack ends up being). The advantage of a higher voltage pack also means supercharging voltages can be higher too and that will help supercharging speeds. I expect the 350KW+ superchargers Elon has hinted at will be limited to the semi packs and any other very large battery packs.
@wdolson question
My S60 bought in late December 2016 and unlocked to a 75 in May 2017.
Do you think that unlocking the battery provided a performance boost? I could not feel it. My question is do you think the firmware or software involved with the DU needs to be flashed or tweaked to take advantage of the additional 15kW from the battery now? Thanks in advance. John
The software locked battery still has the same number of cells as the 75, the software just won't allow them to charge more than 80%. So the peak power the pack can put out with a software limited 60 is the same as a 75. It just won't be able to put out power as long because the cells are charged up all the way when you start.