ADOM (Ancient Domains of Mystery) is a roguelike in which the player must stop the forces of Chaos.
Roguebasin classifies both ADOM and NetHack as Hacklikes, as opposed to Angband and similar games which are Band. So a contrast of ADOM and NetHack is fundamentally different from a contrast of NetHack and Angband.
ADOM and NetHack both have persistent levels (Angband does not). They both have a BUC system (in Angband, curses as such apply only to worn items). They both have gods and alignments (Angband does not). You pray when in trouble. Both ADOM and NetHack shops are rooms with items on the floor (Angband shops are menus).
ADOM is much larger and more difficult than NetHack, while NetHack has some nice features and detail that ADOM lacks. A common summary of the games is that ADOM has more breadth, while NetHack has more depth. Eva Myer's Nethack vs ADOM page has two sections, each listing why one game is better than the other. Nethack vs. ADOM@Everything2.com has three (and potentially more) attempts at contrasting the two games.
Attempting to play ADOM? Edit
NetHack players attempting to install ADOM on their computer (even if they already run other roguelike games) might not expect certain problems that can happen. ADOM's source code is not public and therefore cannot be compiled for Unix or other operating systems. If there is no ADOM binary for your platform, then an emulator such as DOSBox or workarounds such as installing FreeDOS in QEMU will be required.