The Company Secretary role is somewhat anachronistic
The Corporations Law imposes obligations on officeholders, a term that includes directors, company secretaries, and anyone controlling a corporation even if not formally appointed to do so.
Private companies are no longer required to have a company secretary; if they do have one, they must live in Australia. In addition, private companies can have a single director unless they have crowd-sourced funded shareholders, when they need a at least two; the majority must live in Australia.
Public companies must have a company secretary and at least three directors. The secretary and a majority of the directors must live in Australia.
So, legally, there is no difference between the secretary and the directors. For a listed public company, the secretary acts as the point of contact between the exchange and the company and is generally the officer tasked with corporate compliance.
So, in an Australian context, the question boils down to what are the pros and cons of having at least two directors.
Well, for a public company there must be at least three so the question is moot.
For a private company, once the company is no longer tightly held (e.g. by an individual or a single family), third-party shareholders will normally insist on a board seat. So, they normally have multiple directors and, again, the question becomes moot.
For the rest, the advantage of multiple directors is a divergence of views, however, unless some of the directors are independent, there is a risk of group-think, particularly if the directors are closely related. The disadvantage is cost - independent directors expect to be paid.