The overall burning cycle is more efficient. Even with tuning, my old boiler was putting out well over 200ppm CO (down from 2500/off-scale when they first tested it). That’s one source of inefficiency of getting BTUs of heat out of the gas and into the water. As a sibling mentioned, it was also sending 450+°F vapor-laden exhaust up the chimney and out the roof.
New boiler vents through plastic pipe and extracts so much more of the heat that the exhaust is leaving the boiler at around 150°F with the water vapor largely condensed (at least this time of year) and giving up that latent heat of vaporization to the water incoming to the boiler. Additionally, it pulls combustion air from outside instead of the basement. (If you pull combustion air from the basement an equal amount of outside air must leak into the house to replace it.)
New boiler also has a modulating gas valve and can burn in 5 steps between 25K BTU/hr and 149K BTU/hr (from memory, but close enough) to match the space heating demand. The old one was either 0 or 200K BTU/hr.
I probably went from 60% to 95% now plus the effects of not pulling millions of cubic feet of outside air in per year.
The computer controls on this one (and the ability of the boiler to not just tolerate but encourage condensation) mean I can heat my house at 32°F/0°C with 114°F/45°C supply water temps. Traditional boilers are harmed by acidic condensation so need return temps of 140°F which means supply temps of 160°F. That means hotter rads and pipes and more losses in the piping. As it gets colder, the boiler can compensate (via an outdoor sensor) and increase the flow temp so it’s just enough to heat the house. Based on 114°F flow (about 90-95°F return) being enough for 32°F, I'm virtually certain that I'll be operating in condensing mode (return under 120°F) even on the coldest nights we get here or if not, on all but one or two nights.
I have pump controls that can run the pumps for a bit after the zone and burner shuts off to put that (much smaller amount) of trapped heat into the living space rather than leaving it trapped in a massive hunk of cast iron to leak to the boiler room.
It’s a lot of small and medium effects.