'Representing the differences' is not overly specific on the output side of things, espescially as two values must go where the original has only one. A viable solution depends on the consumer of your data.
If it is for humans, you could be done quickly by 'diff'ing output of Data::Dumper.
For automated processing you could walk the structures from bottom to top and prune matching data on both sides. Your application most likely already has a walking algorithm for the specific structure. The result is two smaller structures.
Solving the general case without knowledge of the structure is a lot more difficult.
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