As a general rule "local" or "indigenous" plants are likely to be more reliable in gardens because they are adapted to the local climate. Unfortunately other factors are involved, not least of which is the fact that garden conditions (soil, degree of disturbance, fertilizer use, watering) are not likely to be the same as in the natural environment.
This doesn't mean that the old myth that "Australian native plants can't be grown in gardens" is true; it just means that to grow particular plants, it might be necessary to investigate the required growing conditions and make adjustments to the ways in which the garden is maintained. This is where a local District Group of the Society might be of assistance.
It's also worth considering "how 'local' is 'local'?" because a single species may have a wide natural distribution. Plants grown from seed collected in one location may not produce a hardy plant for another district even though the particular species may grow naturally in both areas and may therefore be considered 'local' in both districts. This is why planting local clones of a species is important.
As an example, the distribution of the small shrub Calyrtix tetragona, shown below, covers a number of climatic zones. Its natural distribution is shown in red on the map. Forms propagated from, say, the dry climate of western Victoria may be difficult to cultivate in the humid coastal zone of New South Wales even though the species occurs naturally in both areas.
Another point in favour of growing local species is that they may help attract the local wildlife (eg. birds and butterflies) into the garden.