logical deduction - Introducing: Compoundoku!

Rules of Compoundoku:

• Solve both left and right Sudokus.


• In addition, the board below them is the Compound Board of both Sudokus.



• Each number on the Compound Board should tell either: (1) the number on the left Sudoku, or (2) the sum of both numbers on the left and right Sudokus; in the respective position.

Answer

I think this is the answer

Partial Reasoning

For starters the 1 must appear on the left and the 6 must be the sum of both.
Once we make a choice of how to split the 6, the rest of the grid is filled in very quickly (4x4 Sudokus are very restrictive). If we put 3 on the left and 3 on the right or 2 on the left and 4 on the right, we can quickly reach a contradiction. However, putting 4 on the left and 2 on the right allows us to complete the grid in a unique way using the logic. A key step is realising that splitting the bottom 4 will eventually produce a contradiction so it must be that a 4 appears in that position on the left.