The Torque Test Channel has done several tests with a single tool using different batteries, comparing (usually) the torque the tool can produce with each. E.g. this[1] with a DeWalt impact driver.
Well I spent too much time on that channel! For that specific test, he is testing no-name batteries against name brand. But there are adapters like [1] that allow you to use another name brand battery in your tool. That test would be the one that matters. Also, if all tools used a standard battery format, there would be much, much higher quality off brand batteries just because aftermarket products for improving performance would make more sense (along with the sloppy cheap stuff, of course).
[1] https://www.amazon.com/ZLWAWAOL-Battery-Converter-Compatible...