DONT OVERFILL
Fuel injection definitely improves economy. On the C182 I've been flying recently it is worth 2 Imperial GPH. This will be partly due to being able to lean it more aggressively without it shaking itself to pieces!
That's a significant difference, over 20%, a lot in anyone's book. Do you really believe fuel injection will make such a big difference?
I have flown several aircraft with fuel injected and carburetted versions of the same engine (all Lycomings) and I have never seen a measurable difference between either induction method.
I don't doubt you've seen a difference however I suspect it's more to do with the relative positions of the black and blue knobs. I've seen some manifold pressure and RPM readings that don't match the real world. A pilot thinks they have X amount of power set by the readings on the gauges when in fact he/she has Y amount of power set, which of course reflects in the fuel burn.
It may also be partly due the the make of engine. The Continental induction tubes are on the top of the engine in the cold cooling air and suffer from poorer fuel air ratio distribution especially for the longer tubes (Carby versions only) as the fuel doesn't stay in suspended in the airflow due to the atomised fuel condensing out. You may not be able to lean as much before you encounter roughness.
The Lycoming induction system comes from a warm plenum area below the sump and the induction tubes run nearby the exhaust system keeping them relatively warmer compared to the Continental. Therefore a carby Lycoming will not see as much variance in air fuel ratio between cylinders.