I guess it's cheaper to not have to install air ducting or indoor units if you can reuse existing pipes & radiators. But if you need to replace the radiators anyway, the cost might not be that much different? You'd get more precise temperature control, and cooling in the summer.
Mini-splits are noisy and have major problems getting heat distributed over a whole house.
In our case we couldn't install ducting downstairs (no space between the floors), but it was simple and cheap to do so upstairs because there was attic / roof cavity space in which to run the ducting.
A big advantage of the mini-split is that it gives you precise temperature control in each room, where as our ducted system only has a single central thermostat, and on/off control in each room. This is problematic for the bedrooms, which tend to overheat at night in the winter when bedroom doors are closed, while it remains cooler in the hallway where the thermostat is. I'm currently looking into an upgraded control system ("Airtouch 5") which should solve this by putting wireless thermostats in each room.