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For example, an ABS-equipped car must be braked differently to a non-ABS car in an emergency situation-many drivers do not realise this. .......
Don't you mean the other way round? :-/ :-/ :-/
Emergency brake assist was dreamt up because Merc? was aware that drivers wouldn't just stand on the brakes & trust ABS to sort it out for them, instead they braked more hesitantly as though they were in a NON ABS car ....... :-/ 
The difference is that in an ABS equipped car, you stand on the brakes and can steer at any stage in the braking time, whereas in a non-ABS car you brake firmly until you feel the traction being lost and then release slightly or cadence brake to lose as much speed as possible and then take evasive directional action right at the very end when most of the speed is lost.
EBA/brake assist was developed to sense when a driver was in an emergency braking situation and was not applying enough pressure for maximum braking, so increased the braking electronically.
Each one of the 87 cars and 16 motorbikes I have had plus endless company cars and coaches and buses I have driven have all had different braking characteristics, but the main difference in braking is the fitment or not of ABS.
Early ABS systems were clumsy and the main issue is with them being over-sensitive; my 2004 Berlingo used to activate ABS all the time, leaving you heading towards the back of the car in front alarmingly, even in traffic!
The main failing of ABS is the fact that it will not recognise snow, gravel and other surfaces where locking the wheels and digging in would be better than ABS taking off the brakes.