Is there a reason to choose one over the other?
If all the functionality you need are present in both, and if those are the only two choices you are considering, InDesign is a higher quality program. Illustrator is very long-in-the-tooth and has a cluttered, scattered, and confused interface.
But it depends on what kind of projects you intend to do. InDesign is a conventional-wisdom page assembly program. As such, nearly everything in it is designed to facilitate repetitive design tasks for "bookish" whole documents of relatively high page-count with repetitive layouts.
Illustrator is a conventional-wisdom vector drawing program. It's aimed at creating individual illustrations (for placement in InDesing or some other conventional-wisdom page assembly program, and/or non-repetitive low page count whole document layouts (the ubiquitous two sided brochure, sell sheets, etc.) and (now) sets of related project pages of different sizes.
For a complete toolset, the usual breakdown includes:
A vector drawing program.
A raster imaging program.
A page assembly program.
Thus, the logic behind the various Creative Suite bundles. Being Adobe, you add Acrobat Professional to help facilitate final delivery and multi-purposing. If you do web work, you add Dreamweaver as the web-centric "page assembly" program in lieu of print-centric InDesign.
(The frequency of this kind of question is telling. It reflects the poorness of product-definition so common today, especially in the software industry. Poor product definition delays--and sometimes prevents--buying decisions. For example: I've always considered Dreamweaver to be a most idiotic product name. Tells you nothing about the product. Sounds like a matress.) ;-)
JET