Just like it is easy to import PSD and AI files into InDesign, it is also easy to export InDesign artwork into either of these programs. The simplest method to do this is copy and paste. The procedure is the same for both the programs but keep in mind that the objects’ paths in InDesign are more appropriately imported into Illustrator to retain the vector paths rather than in Photoshop. Photoshop rasterizes the image so you are left with fewer editing options.
It is always recommended to first import the InDesign artwork into Illustrator and then take it from Illustrator to Photoshop.
To copy the InDesign artwork, simply select the desired objects using the Selection tool and press Ctrl+C on Windows or Command+C on the Mac to copy the objects to the clipboard.
Create a new Illustrator document and press Ctrl+V on Windows or Command+V on the Mac to paste the InDesign artwork. You will notice that all the vector paths are carried over to the Illustrator document and you are also able to scale freely without loss of resolution.
However, while pasting the same artwork in Photoshop, you will see that there is loss of resolution and the image gets rasterized. It is still pasted as a vector smart object but in order to change the paths, you need to go back to Illustrator, change the paths, save the file and come back to Photoshop.
Therefore, it is always recommended to import InDesign artwork into Illustrator than Photoshop. If you must use Photoshop, then import it into Photoshop via Illustrator but never paste directly.