InDesign and Illustrator are both great programs for creating impressive visuals for web and print. Each program has its own advantages and can be used for different tasks.
InDesign excels at layout and document publishing, such as books, magazines, and flyers. It also gives you a lot of control over typography and controlling the overall look and feel of a project. InDesign is best when you're creating multiple page designs that need to be connected in a logical way.
On the other hand, Illustrator is more geared towards vector artwork, such as logos, illustrations, and other graphics. It's also a great tool for creating complex illustrations. Illustrator is great for objects that need to be resizable and sharp, since everything is a vector, you can blow it up as big as you want without losing image quality.
In conclusion, it really all depends on what kind of project you're working on and what your design needs are. Both InDesign and Illustrator can produce stunning results, so it pays to know what features each program offers and how best to use each in order to produce the greatest final product.