You notice a difference in the engine and acceleration.
The Eco mode does not make any difference to the fuel economy.
I tried this out, when i was doing an 80mile round trip daily.
I did one day in eco mode, one day in Normal and then in Sport.
Eco and Normal I saw NO difference in economy over the same trip.
Sport used a little more, 2mpg difference.
Pressing the sport mode, puts the gearbox into sport so it stays in a lower gear for longer, to aid acceleration through the gears.
Eco mode changes up quicker than Normal mode, but you have to give the throttle more to get going, so its not really a benefit unless you have a nice open road.. and WHO has that in the morning going to work.. Certainly not around where i live.
So I mostly leave the car in Sport, but move the gearbox back into Normal drive mode. So engine, Acceleration and steering are all more responsive.
and if want to go full sport just pull back the dog leaver and it changes to sport mode.
and I have found that changing the mode between Normal and Sport, does help, as sometimes the car does not want to accelerate or gear change in not so smooth, so change the mode and it calms down again..
That is what i have found with my Golf.