Sports mode shifts at a higher RPM than the regular. I’ve been trying to figure out how much difference that makes in how the car drives. Is it just me or is the car more responsive/faster to accelerate in sports mode?

I ask because someone suggested that sported mode mode makes no difference in acceleration and only really makes more noise.

 

Mazda Skyactiv engine and transmission:
When in sport mode the ECU adjusts the drive-by-wire so the feeling may translate to some drivers as faster or quicker feeling. The protection for over revving is still there and there is nothing to much more as far as engine operating changes in the ECU when manually shifting. So any feeling of greater power or quicker engine responses is only how you are now throttling and shifting the transmission.
I neglected adding and was asked via a PM (thank you for the question() to mention that the gear prolong RPM shift perimeters do slightly change regarding the transmission controlled operation in the ECU but very little.
The only real way to get true manual shifting increases is with getting a program like VersaTuner however even without advance calibration experience very few do this because of the time building transmission maps shifting calibration maps to altered from the OEM Mazda ECU programing.