Dyno runs done by Evolve on a stock G80 Competition, a stock F80 and stage 2 F80.
The S58 turbos spool around 1k later than the S55 so they are significantly bigger = more HP up top. S58 also has a lower compression ratio of 9.3 compared to 10.2. They probably done this to reduce NOx however it also means you can push more boost safely without knock.
This explain the turbo lag however it is the perfect recipe for SERIOUS whp with just turbo supporting mods and a tune.
BMW engineers knew exactly what they were doing. Gotta love em.