Wikipedia states:
However, where his father's preaching tends to be heavier on psychological reference and lighter on scriptural reference, Robert A. Schuller's messages rely considerably on scriptural reference, hermeneutics, and apologetics, making the role of "positivism" secondary and more in line with mainstream evangelicalism.
According to this and this, Junior was sacked because of a "lack of shared vision and the jeopardy in which this is placing this entire ministry."
Reading between the lines, it appears Junior simply failed to attract the necessary audience (and donors) to the TV broadcast which sustains the church during his three year stint at its helm.
The younger Schuller blamed the program's format and wanted to change it in in a manner which would supposedly make it appeal to a younger audience. The older Schuller felt the show's format was just fine and blamed Junior for failing to deliver the ratings. The older Schuller won the boardroom battle.
Bottom line: It was money, not doctrine.
You said — “I would love to hear the details on what differences they have...specifically why he fired his son.”
That quote that you included from Wikipedia, is also what I read elsewhere, as to the cause of the split. It seems that a more conservative approach to the Bible (by Schuller’s son) was too much for the elder....
In that case, good riddance for the Crystal Cathedral...