The savings come down to a bunch of factors.
Depending on what type of furnace you had prior. A single stage, vs a dual/tri/multi stage.
A single stage will come on full black, so say 100% input of gas.. and heat up and blow till the temp is reached.
A multi stage, starts at a lower setting (say 30%) for a period of time, and if its reached temp, then stop, if not, ramp up to the next % level). I think these ones can take a little longer to heat, but could reach the heating up target temp with using less gas.
(assuming that your not going from like ice cold.. just a normal few degree change)
And then everything else going on in the house as well.
How good the insulation is in the walls, the attic, etc. The seal on the windows/doors, etc.
Anything that bleeds heat.. the furnace will run more too
We had an old 20ish year old when we moved into our current house. It died within 6 months of moving in. The newer multi stage, we save somewhere between 20-25% difference on the gas bill from when we moved in. (but we also upgraded from the builders crap windows to brand new ones, etc at the time too)