I think you will find that each State is different and each Council is different so no easy answer
Also although in the past Councils adjudicated between neighbors over fences, trees etc these days they go in the opposite direction very fast
So your question is a IMHO a purely legal one between neighbors ie get a good lawyer (if there is one)
Look at any residential area and you will see inappropriate planting and inappropriate style of plants which were never suitable for a residential block in the burbs
Do the neighbors plants interfere with your drainage ? If they do you may have a case ?