There can be a difference in meaning between the constructions "of noun" and "adjective". In this case, "of interest" can be used to describe what an individual considers interesting but can also be used in a broader scope to describe what an organization or society finds notable. In contrast, to find something interesting is a personal activity. For example, being a "person of interest" (to law enforcement, perhaps) is very different from being an "interesting person".
This work is of great interest (to me, my friends, the field, or society)
This work is greatly interesting (to me and perhaps to other individuals).
The software will be of interest to schools and museums.
X The software will be interesting to schools and museums. (This use does not sound natural because schools and museums are being overly anthropomorphized; a school or museum cannot sense interest.)
Warrington Council has recognised the building as being of historical interest (to society or the region).
Warrington Council has recognised the building as being historically interesting (to historians or visitors). (This use sounds slightly less natural because it sounds odd to certify that people will react a certain way. However, "historically interesting" is still commonly used to mean "of historic interest"; Google counts the former as being used about half as often as the latter.)
The last two examples are essentially equivalent:
The story was of particular interest to me as a New Zealander living in Australia.
The story was particularly interesting to me as a New Zealander living in Australia.
In the other example, "of a difficult nature" is ambiguous because the families are encountering difficulties, but the people taking the calls may also find it difficult to listen to stories of extreme hardship or find it difficult to organize large-scale help. Some clearer examples using the adjectival form are:
It was difficult to listen to so many calls from distressed families with moving reports of missing people.
The emergency team found it difficult to respond to so many calls from distressed families with moving reports of missing people.