Short: Essentially the power limiter is a torque limiter wherever the horsepower would exceed this value: (peak*limiter). A car with a flatter power curve with 5-10 less horsepower has the advantage because of a wider power band.
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Long:
Consider two scenarios, given multiple cars with the exact same aerodynamic properties and weight to control this.
Car 1 has an engine that has a flatter power curve at high RPM, its peak hp being 350 from 7000RPM to 9000RPM.
Car 2 has an engine with a slightly higher peak hp, but a shorter "power band", so to speak, its output ranging from 330hp to 370hp from 7000RPM to 9000RPM.
Car 1's power curve (plateau) is more desirable in this case. He's able to more reliably access his power without as much regard to shifting at an exact point on the power curve. As long as he makes is so the engine is at 7000RPM after he shifts up, he's lost no potential acceleration capacity.
Car 2, on the other hand, needs to worry about where he's shifting to make his power curve work, and he's also got to have his gears matched up to aid in tapping that power. He has more potential accelerating capacity for a short period of time, and in other places he's lagging behind.
Now then. It doesn't matter if Car 1 is at 7000 or 8500 or 7250 RPM on his power curve. If torque was all that mattered on cars, then we wouldn't care to measure power. Since power is a function of work done over time, we are interested in it when speed and acceleration come into play. Torque is important, but when we want to achieve high speeds we are not interested in where the car is making the most torque. We are interested where the most horsepower is being given.
Onto the matter at hand. You were taking a car with two setups with the same PP. The one without a turbo presumably had a higher peak horsepower output, from my understanding, because the game also takes power band width into account. The reason you experienced similar acceleration on both setups is because one reached its peak output earlier and flattened while the other build up more but eventually went higher. They both came out roughly the same in this case.
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A car seems to "pull" when it's accelerating out of low RPM because of the increase in HP toward its power band. In some cars this is a very steep climb in a short period of time.
A car's wheels will spin more easily if you launch it at peak horsepower instead of peak torque.
A car's aerodynamic top speed is more easily gauged when you aim to have that aero-limit in the power band.
Focus on horsepower, not torque. Torque is important, but we're interested in how much work the engine is doing to move the car in a given period of time. That's horsepower.
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Edit 1: As the person above me said, it's track-specific. Peaky vs. Flat depends, though I'd always recommend just a tiny bit of flattening on the curve. Maybe 0.5% to 1% at the least, if you can manage.
Edit 2: If two cars of the exact same weight and aerodynamic properties have the same torque at the same RPM, they will accelerate just as fast. If they have the same torque at different RPMs, then one will accelerate quicker. If they have different torque at the same RPM, then one will accelerate quicker.