Oversizing high-mass boilers by more than ~1.6x has a damaging effect on the average operating efficiency. If it's literally 5x oversized (as it might be based on your neighbor's boiler sizing), you can take at least 15% off the steady state efficiency (BTU-out divided by the BTU-in) as an estimate of the as-use AFUE, eg:
Say your actual design-condion heat load is 40,000BTU/hr, but your boiler has a rated output of 200,000BTU/hr, with 250,000 BTU/hr in for a 80% steady-state efficiency, the true as-used efficiency is not likely to exceed 65% due to high idling losses during the shoulder seasons (even for cold-starting boilers.)
The greater the degree of oversizing for the actual loads, the worse off you are. AFUE testing is at a duty cycle that presumes 1.6x oversizing and a low operating temperature for minimum idling & cycling losses. Take a look at the regression curves in the appendices for the boilers tested by the Brookhaven Nat'l Labs in
this document, and consider how far to the left of the curve you are if the peak load is at the 20% mark (5x oversizing), which puts the average load for the season somewhere in the 8-12% range.
Then consider that corrosion &/or scale on the heat exchanger plates have knocked on the order of 5% off the steady state efficiency, so that 80% boiler is really 75%, and at 5x oversizing you're getting maybe 60% as-used efficiency.
Most hydronic boilers at the age of 70 would be struggling to hit better than 50-55% efficiency. If it's a steam boiler it might not even be that good.
A new right-sized mod-con boiler can deliver north of 90% as-used efficiency, and would be a good investment were the boiler your primary heating source. But in a D.C. climate the mini-splits deliver PHENOMENAL shoulder season efficiency, and pretty-good mid winter efficiency. If the mini-split is handling 75%+ of your heating load or more there's little financial incentive to change, and you may still get better bang/buck out of a programmatic approach to air-sealing and insulating to reduce the load. A new mod-con and heating system tweaks could easily run $8-12K, which buys a lot in terms of air-sealing the basement & attic to kill off stack effect infiltration, and spot-insulating where there are gaps. Most of the older homes in the mid-Atlantic states would leak more than 8 air exchanges at 50 pascals pressure in a blower-door test before an air sealing effort, and if that leakage is concentrated at the basement (foundation sills & band joists are notoriously leaky), and the attic (recessed lights, balloon framing, plumbing & electrical chases & penetrations), the impact on heating energy use is significant.
Most homes in the mid-Atlantic region also have no foundation-wall insulation, which will account for a double-digit fraction of the heat load & heating fuel use in a multi-story house, often over 20% for a single or 1.5 story house.
If an equivalent amount of weatherizing can bring the design condition heat load within the output range of the mini-split it may be worth mothballing the hydronic heating system. But if you're committed to hydronic heating, the first and most-important aspect when considering a new boiler is to get the sizing right, with a room-by-room Manual-J or I=B=R type heat loss calculation, base on the realistic
99% outdoor design temperature, with minimal or no oversizing. A right-sized 85-88% sealed combustion cast iron boiler can be a significant cost savings over a mod-con up front, and would still deliver a significant fuel savings below heating with a 5x oversized boiler.
To calculate your average heating costs with the mini-splits vs an oversized boiler running 65-70% efficiency, we'd need to know your electric rates (total bill divided by the kwh used) and your gas rates (total bill divided by your therms or ccf or decatherms, however it's done under your utility.) Unless your electric rates are significantly higher than the national average or your gas rates lower, it's likely that heating with the mini-splits will be cheaper. No matter what your rates are (barring island community 50cents + electricity) the mini-splits will be almost certainly be cheaper to heat with whenever it's over 40-45F.