The question is are you more interested in efficiency or comfort?
There are all kinds of high efficiency systems out there to replace your boiler. From what I have been able to determine, most of them are complete crap.
My house was similar to yours, built in 1960, and had a gas fired boiler furnace with baseboard hot water heat. The boiler furnace also supplied the domestic hot water, but that’s a separate issue.
I like baseboard hot water heat. I think it is the most comfortable type of heat. So for me there was no question, I wanted to replace it with another gas fired boiler type of furnace.
In my case, my original boiler furnace also supplied the domestic hot water, so instead of a separate tank like you have, the furnace simply had a second coil of water pipe going through the furnace core. The furnace keeps its core hot, the hot water through the house is heated by going through the core, voila! Endless hot water. The furnace can heat the entire house, so it has no problem heating the incoming cold water up to hot water temperatures for use in our bathroom and kitchen. There’s no tank like in the systems you describe.
The benefit is that you always have hot water. My kids could all take long showers, but since the furnace is heating the hot water on demand, we would never run out of hot water.
The down side of this is that the furnace core is always kept hot, even in summer. So it’s a much less cost-effective way of generating hot water. It’s not hugely expensive, but there are cheaper ways of getting your home’s hot water.
But I personally preferred this system, especially since another benefit is that the hot water would last as long as the furnace, where separate water heaters only tend to last about 10 years or so these days.
The furnace is now about 15 years old and it’s still working great. I’ve never had a problem with it. It’s also about 1/3rd the size (physical size) of the original furnace while providing the same BTU output.
I personally prefer comfort and convenience to cost. YMMV.