With ASR when one wheel starts slipping slightly, that wheel is individually braked - consuming both brake thermal capacity and using up engine power that could be transmitted to the other wheel.
..but it does work better than nothing.
With a Q2 mechanical diff, the power that is causing the wheel to spin up is shifted to the wheel that has more available traction (up to a certain max split of power, around 2.5:1 ).
So the engine is used more usefully, and the brakes aren't needlessly being heated.
The ASR will also automatically reduce throttle if more serious wheelspin is detected in which case it also wont attempt to brake an individual wheel..
This is fine for normal driviing, but a keen driver would be able to modulate the power better with ASR switched off - especially for quicker reapplication of power once you have eased off.
Finally the ASR can work in conjunction with the Q2 diff too, but it will be working much less often. With a good diff like the Q2
you can mostly at this point get the same effect by easing off the throttle yourself..
Hope this helped
What's the difference between the Q2 and the ASR? (sorry for asking so many "simple" questions).