Hello szembek, welcome to the forum. The big advantage of a boiler is that the water can store a lot of heat, and not have it get distributed throughout the house. If the house thermostat is satisifed, and the air circulation fan shuts down, the coal fire doesn't just imediately cool off in the furnace, the coal keeps burning [slowly making less heat] and the furnace gets hot, and it has overheat protection so the air circulation fan will come on and move the heat into the ducts to keep the furnace from overheating.
With a boiler, the air circulation fan turns off, the coal fire slowly makes less heat, but the water can rise in temperature, storeing a lot of heat before any overheat situations arise. The other nice advantage is a boiler is real easy to use to heat your domestic hot water as well as the house. This is an additional savings in oil, gas or electricity used.
A boiler can be placed just about anywhere, there only needs to be two pipes running from the boiler to the heat exhanger in the air plenum. So there is very little ductwork modifications to hook up a boiler.
During warmer weather , a boiler can idle all day, using very little coal, putting no heat into the house, then fire up for the cool evenings within about 20 minutes. With a furnace, you will have some residual heat getting into the house during the warm days, making the house too warm.
So a boiler can be used earlier and later in the heating season.
Hope this answers your questions Greg L