Here are some suggestions about what InDesign would be best for: Any multi-page project (Illustrator only does single pages); any project with much text (InDesign's text handling is much more powerful); projects with many placed files (InDesign's import filters are stronger). InDesign also has preflight/packaging which Illustrator does not. This would be my first choice for most publications.
Illustrator is stronger when you are editing paths (it has more tools than ID, but ID has the more common one); ability to apply effects, graphic styles, brushes, symbols, envelopes. You can always create artwork in Illustrator, save as an AI file, and placing in InDesign.
If you're more specific about what kind of print output you do, we could help you more.