Mercedes-Benz claims power increases from 451 horsepower to 481 horsepower but in practice it seems to be even stronger than the MB claims. Just look at this race between a stock P31 C63 AMG versus a tuned standard C63 AMG with filters and a cat delete. Mercedes-Benz offers very aggressive factory software for the P31 cars.
Due to how aggressive the stock software is many tuners struggle with improving upon the tune. The P31 tune is so good some (now somewhat defunct) tuners would flash the stock Mercedes P31 software onto C63's. What shows skill that separates tuners is things like getting extra power on P31 cars.
Check out the race below between two P31 equipped C63 AMG's one of which is tuned by Weistec. The tuned car takes the P31 car significantly up top showing a horsepower difference. Keep in mind that the tuned car which pulls has the MCT transmission while the other P31 car (due to the option coming on the market before the MCT was featured in the C63) has the 7G transmission. It is definitely a factor but regardless horsepower wins this race.