As it is now, the programs are barely compatible, and this has been the case since the existence of both programs.
By @desgnRuub
The programs are completely compatible - they don't work the same way, and they don't perform the same tasks. If they did, there would be no need for separate programs.
Layout shlould be done in InDesign, with placed pixel images from Photoshop, and placed vector images from Illustrator. This has been the case since the existence of [all three] programs.
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