I look at it from a productivity point-of-view. As far as quality is concerned, there is no difference as long as the documents and the applications are setup properly. I find a general rule-of-thumb works good for me. It goes something like this: for one page documents and logo / illustrations / gradients, etc., Illustrator is superior...much faster and more efficient. For multi-page documents ( i.e., newsletters, catalogs, magazines, books, etc., InDesign or QuarkXPress is better. I've seen where it may be advantageous to Place live .ai files in ID; but .eps is acceptable, too. Live files may have raster effects and transparency that will not flatten until it gets to the RIP. But, there really is no right or wrong answer here. It may come down to what you are more comfortable with, period.
like john said, there really isnt a difference with quality. there difference depends on the comlexity of the project and the final project.
for business cards, tri-folds, flyers postcards etc, even catalogs under 8 pages or so, I'd recommend AI.
For myself, these items are usually more graphic and color oriented. This involves blending, effects and working with mulitple layers. AI is great for this.
Even if the project, say a quad fold or a 8 page catalog(which is only 2 SHEETS of paper. 1 body plus self cover) can be easily laid our using artboards and making guides.
Hit set all your guides( fold lines, bleed and print safe edges) on 1 layer then lock it. This will prevent you from grabbing and moving them by mistake.
For more involves projects like a catalog over 8 pages, then ID is the way to go. It will layout the project for a printer much easier and will allow you to easily then duplicate the project as a digital brochure too.
Otherwise for anything other than catalogs, id go with AI. for signage etc, you can make wireframes etc and i personally like working with it.
In the end though, most of adobe is interchangable so really if its not specifically a ID or AI item, just go with what you know best.
Since quality is the issue that you are most concerned about, both will actually do. The reasons are very well laid in the previous responses.
I agree with John. Illustrator is easier and faster for one page documents whereas Indesign is better multi-page documents. I really don't see a difference in print quality between the two, but the again, I use Illustrator 90% of the time because I'm usually creating 1 page docs, so I haven't compared the two all that much yet.
i have used illustrator big time but for my case i wouldnt usecthe quality i will say neatness indesign does better