Am I right in thinking that a generic map yields bigger gains on the tsi engine?

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Yep. Stage 1 on tfsi is circa 235bhp and circa 245bhp on tsi.

But the stock curves are identical? I have seen occasionally 210bhp against the TSI spec, but the official vehicle specs state identical power and torque values.

What about torque, and more importantly the engine speed at max bhp and torque?