I have an inDesign document with some text plus a few illustrations done in Illustrator. The colors look great on my PC, but is very bright and weird on both iPad and smartphone (Galaxy S3). Then I tried to export with Destination: sRGB IE61966-2.1, which made it look quite good on my iPad, but still very bright on my smartphone...
Is there any better Destination for exporting, or something I can do to ensure good consistency with the colors?
Sorry, smartphones and tablets are NOT color managed. Therefore, exporting with profiles will make no difference whatsoever. You're at the hands of the device display gods. Do a prayer before you send it off. ;-)