2 of my relatives have Honda City and one is using 1.3 and the other one is using 1.5 and the one with 1.5 always have a better fuel average on his meter.
Though fuel average totally depends upon how the driver is driving the car and how hard the foot is applied on accelerator.
But still there is one simple physics that if you have to move same amount of weight the one with bigger engine will have to put less effort hence resulting in less fuel consumption.
Now please don't give example of civic as it's a different breed because it's tuned differently and it's purpose of built is never fuel economy. Where as city is tuned for economy.