I think this video sums up the power shift in rugby union.
To sum it up, South Africa and New Zealand dominated the 20th century because they selected players from provincial teams. Australia and the other countries selected their players from lower standard club competitons.
Queensland and New South Wales didn't many games throughout the bulk of the 20th century. This changed in the 1970s when the Queensland team began to play more games than any other province in the world. Queensland started to dominate New South Wales during this period and it lead to Australia's rise in the 80s and 90s.
ACT joined Super 12 with a team that had a lot of experience playing alongside one another. The Brumbies and Reds were largely responsible for Australia's dominance in the late 90s and early 00s.
The problem for Australia is all of this broke down when the ARU expanded into Perth and Melbourne. It weakened the Queensland side the most and broke up player combinations. When Australia was winning they had thw most experienced player combinations in the world, with players lining up alongside one another for their states and clubs long before winning a cap for the Wallabies.
The Celtic nations went from having lots of clubs to fielding a few provincial teams in a new competition in the early 2000s. Before this happened the previous fourteen Six/Five Nations titles were won by England and France on 12 occasions. Since then Wales and Ireland have won more titles than England and France.
New Zealand and Australia have been hurt by professional competitions in Japan and Europe stealing their players.