It would indeed be tempting to say that these two constructions are effectively one and the same, but there are some instances where you simply cannot use them interchangeably. The subtle nuances are easier to grasp when they are translated into English.
= Most fruits are round. [adjective-ish]
= Fruits are almost always / in most cases round. [adverb-ish]
With this in mind, let's take a look at the following example:
[Grammatical]: ... その原因のほとんどは運転手のミスである。
= They are almost always / in most cases caused by ... [adverb-ish]
In this specific instance though, you cannot switch the words around and use the adjective-ish construction ほとんどのX:
[NOT grammatical]: ほとんどのその原因は運転手のミスである。
= Most their causes are ... [adjective-ish]
It is the word その [its/that/their] that makes this adjective-ish construction impossible here.
Bear with me here, as I have intentionally used clumsy English phrasing "most their causes are" for the sake of better capturing the feel of the Japanese sentence.