Both Photoshop and InDesign by default will preserve and honor all embedded color profiles. So as long as your placed files have embedded profiles - and you haven't changed anything in the apps' Color Settings - they should be absolutely identical.
Both Photoshop and InDesign by default will preserve and honor all embedded color profiles. So as long as your placed files have embedded profiles - and you haven't changed anything in the apps' Color Settings - they should be absolutely identical.