In reality, since the implementation of multiple artboards in Illustrator the reason for using Indesign compared to Illustrator changed a bit. Pre CS4 the immediate reason was a single Indesign document rather than separate documents for each page with Illustrator.
Nowadays, there are still reasons one may prefer Indesign over Illustrator but, similar to the Mac OS vs Windows, the reasoning is often based more on preference than actual hard limitations of either app.
Few of the items below are black and white, right or wrong, reasons. Rather they are more strengths in the particular app. There is some crossover and some items possible in Illustrator are possible in Indesign and vice versa. The primary difference is which app has a stronger code base for a particular feature set.
Indesign benefits:
Better text handling. Indesign handles a lot of text editing much, much easier and more fluently than Illustrator. While some of the text features can be similar between the two apps, only Indesign has a story editor, column settings, column splitting/spanning, grep searching, etc. Setting massive amounts of text in Illustrator can be a lesson in frustration due to how little management over columns Illustrator contains. In addition things like Character and Paragraph styles in Illustrator are, to me, backwards. AI : Paragraph style dependent upon Character style. ID : Character Style dependent upon Paragraph style. Indesign's text engine is simply more intelligent and better developed.
TOC and indexing. Indesign contains automated tools to control a Table of Contents, indexes, hyperlinks, bookmarks, etc. There's absolutely no such tools in Illustrator.
Master Pages. Indesign's master pages far, far, outweigh anything in Illustrator which may have similar functionality. In reality, all you can do with Illustrator is symbols and a common layer. Not anywhere near the master page logic in Indesign.
File sizes. Since Indesign is a "container" app it doesn't store images and placed artwork within the file. This allows for much smaller file sizes in general and the ability to use one image file for multiple documents rather than having to embed the same image data in multiple files. I'm referring more to embedded images in Illustrator or original artwork in Illustrator. Illustrator, does of course, have a link option. But many things need to be embedded within Illustrator to achieve desired appearances.
Output. From a single Indesign file I can export or save to a wide variety of necessary formats with little post-processing. For example one Indesign document can create a press-ready PDF-x1a file, an interactive pdf file, or an epub file. Illustrator will save to PDF, but forget about epub or interactive pdf.
Illustrator benefits:
Easier custom layouts. It's much easier in Illustrator to create layouts which have some variety in both object placement or trim dimensions. For example, an oddly shaped piece where a die cut is needed is easier to see and use in Illustrator than it is in Indesign. It's not impossible with Indesign, it's simply easier with Illustrator.
A perceived design freedom. Illustrator, and the nature of the object-based elements, lends itself to an aire of less restriction. Allowing a user to more quickly draw, paint, or rough out something then refine it. With Indesign it's often a matter of needing to plan the layout first, then implement it.
More visual versatility. This may simply be my opinion, but I find the ability to alter the appearance of any item much easier within Illustrator. This is primarily because Illustrator is a drawing tool first then a layout tool second. Where Indesign is a layout tool first, then a drawing tool second. Things like custom designed headlines go much faster with Illustrator, and even faster than if one were to create them in Illustrator and place links in Indesign. Things like Text on a Path, or envelope warping, are much easier within Illustrator as well.
Drawing tools. While Indesign does contain some basic drawing tools, they are rudimentary when comparing them to Illustrator tools. This may not be a "deal-breaker" where layout is concerned however. It depends a great deal on the desired appearance. I've created layouts in Indesign and used the drawing tools there for some simple items. Using Illustrator simply makes more sense to me if a layout is highly illustrative in nature.
Since the release of CS4 I've relaxed a great deal on which tool should be used. I used to be adamant that any document containing more than 2 pages should be done via Indesign (Or XPress, heaven forbid). However, with multiple artboards in Illustrator I've found myself using Illustrator for very custom layouts where it simply makes more sense to have the freedom of layout as opposed to beefy text handling.
The decision for me has now become,
"How much text handling do I need here?
An Index?
Page Numbers?
Table of Contents?
Active hyperlinks?"
As well as,
"What output is needed?
PDF?
epub?
Interactive PDF?"
IF I answer "yes" to any of these, I'll still use Indesign just to make my life easier. However, if I'm asked for a poster, simple brochure, flyer, etc. I have no issue using Illustrator for the layout. I still tend to jump to Indesign if a project contains more than 2 signatures. But anything with 1 or 2 signatures I'm up in the air about which app I'll use until a design has been roughed out.
file > place) the Illustrator files (don't panic that they look pixelated - Indesign shows low-res previews to save memory). Then gradually phase in features of InDesign as you learn them. A good first one is to add the block text text boxes in InDesign, and get used to its type features like linked text boxes and character/paragraph styles.