There's a very interesting listening experiment to be had here.
Why not try listening to Schoenberg's output in the order that he wrote it?

I've often read that you can very clearly hear the progression (so it doesn't sound as drastic as 're-wiring') from one piece to the next (and when you're thinking about Wagner, don't forget Brahms 'The Progressive').
We so often listen to music out of chronological sequence that we sometimes try to make sense of an entire composer's output in one mouthful.
Comparing the Stravinsky of the Symphony in Eb with the Variations in memoriam Aldous Huxley, for example, renders two very different composers.
How about Shostakovitch's 1st vs his 15th?
There are clearly audible links but at the same time there's a whole lifetime of experience informing the later works.