I think one of their main advantages is to heat multi buildings at one station. The most efficient ones use maybe a little bit more wood as a wood stove sq footage ratio wise. The not so efficient ones can use double the wood. Other advantages is they are cleaner for the house environs in not only keeping the wood mess outside, but also not breathing in the particulate matter of a wood stove inside the house.
Boilers aren't for everybody, and there have been some badly made ones.
Depending on where you live, external boilers may be easier/cheaper to insure since combustion is external to the dwelling. Dual pipes are pre-insulated, all in one tube (think O pipe diameter), so are efficient and easy to install. They can be useful for retrofits, using a heat exchanger on a forced air setup, and not just radiant/slab heating. Useful for initial or primary domestic hot water heating. Ash is already out of the house; you don't haul wood inside.
Boilers don't make much $ sense for heating a small well insulated space. At the other end of things (space wise), they can make a lot of sense. Attractive in the Ag world, for heating greenhouses. They (Portage and Main) have a large setup for an external (to the boiler) hopper for wood chips, auger driven - for large scale operations that are already dealing with chipped wood, this can make sense.
Like tractors
Rgds, D.