It’s a very hard comparison whether to use Adobe Illustrator or Adobe InDesign for design purposes. Actually, both applications have different uses. There are far great features for illustration in Illustrator, obviously Adobe Illustrator is made for vector illustration purposes than Adobe InDesign, but on the other hand Adobe InDesign is most useful when you are dealing with large documents, for example, if you have to design a document having more than, let say, 20 pages or more then your first choice should be Adobe InDesign because its so easy to keep tracking of page numbering, headings and body text styles, chapter markings etc. which is almost impossible to handle in Adobe Illustrator specially if there are continuous bombardment of changes like additions and subtractions or heading style changes from the client.
Both software programs are necessary for graphic design echo system especially if you are a graphic designer with multiple talents of vector illustration and publishing.