QuarkXPress is the world's most widely used and advanced publishing software for all kinds of publishers. Its achievements in terms of print design almost the same as PhotoShop's in the field of graphic design. BTW, it has 30 years of history.
Adobe InDesign is a DTP (desktop publishing) application developed by Adobe Systems company, which is mainly used for the typesetting's editing & designing of all kinds of presswork. It is released aiming directly at its rival QuarkXPress. Although initially faced some difficulties in attracting customers, yet it had begun to catch up with and surpass its competitors after the Mac OS X edition released in 2002.