But regarding the question of which tuners guarantee to deliver more meaningful/better software than what a well-designed power box offers, unfortunately, this doesn't help us at all

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Hi,
A power box can never be specifically tuned to a particular car, because there are always tolerances in the engines, and every mass-produced engine reacts slightly differently to performance enhancements.
Therefore, you have to drive the car, adjust the settings, test, drive again, etc.

until it works correctly, and thus make fine adjustments – only then is the software specifically tailored to the car. Everything else are mass-produced chips that are only roughly adjusted.
'So, my tuner assured me that he can achieve a much better and more precise result if he modifies the original engine control unit.'
Regards,
DJ.