I do this a lot: I have a diecut in Illustrator and need to create the layout in InDesign. I have a little OCD (like most DTP/Artworkers :)) ) so I create the diecut in Illustrator and then fit the artboard size to the whole art. When I start creating the layout in InDesign, I create the document using the same page size as the Illustrator file. And I do this several times a day. :)

It would be great to have an option/button in Artboard Tool (Illustrator) / Page Tool (InDesign) to copy the size and be able to create a document with the same page size in the other program. I'm thinking something similar (not the same) to the Photoshop default option of creating a new file with the same size as a printscreen/copied image.