There were a variety of clashes over the years but it all came to a head over the 2003 world cup.
Vernon Pugh (Welshman, former IRB chairman) wanted to take it off of Australia and New Zealand and give it to the French (who were ready at late notice having recently hosted the Football world cup). To do this he sprung a clean stadium requirement on them late notice, the kiwis were unprepared and had to pull out from the matches they were going to host, but O'Neill had prepared for it and was ready for Australia to step in and host the whole thing.
It is more complicated than that and there were a lot of dynamics at play around the shift to professionalism, but that's what I've always been aware of as the biggest issue. Most of the major players from that period are dead or dying though, it's hard to see how it could have much ongoing impact. There's plenty more recent issues for them to all fight over.