Is there any reason that different files would display colours differently, not just in the document but also in the colour windows?
Yes. The assigned CMYK profile and to a lesser extent the Color Settings Conversion Options will affect the display (the conversion of CMYK values to monitor RGB) or a conversion to a chosen destination RGB profile. The destination RGB profile will also affect the final numbers when you convert CMYK color to RGB.
In InDesign the frontmost document's CMYK profile assignment will also affect the document's swatch previews. The difference can be slight or obvious depending on the profile assignments.
Here's your CMYK color with US Sheetfed Coated vs Coated FOGRA27 (I've set Photoshop's document info to Document Profile in lower left corner):
Thanks for your response. It turns out that despite both files having identical options selected in the Colour Settings dialogue box, there was a difference in the Assign Profiles settings. The older file had the CMYK option "Assign Profile: US Web Coated (SWOP) v2" selected rather than "Assign current working space: Coated FOGRA39" etc.
despite both files having identical options selected in the Colour Settings dialogue box
Right, syncing your Color Settings usually has no affect on existing documents. A document's profile assignments and policies are set at creation.