"Which is better, Nethack or ADOM?" is occasionally a hot debate on the Nethack or ADOM newsgroups. Personally, I play and enjoy them both. I'd say that Nethack does better on small details, having a plausible response to everything the player could conceivably attempt to do (including strange and useless actions like level-teleporting to a negative level). However, ADOM does better on large details, having a more complex plot and a much larger gameworld with plenty of useful NPCs. This page discusses in detail where I think Nethack does better than ADOM and where I think ADOM does better than Nethack. It might contain minor spoilers for both games.
Nethack has the #name command, an excellent feature which IMHO ought to be available in every roguelike. This command can be used to name an individual item (for example, to note that you think it's cursed), but its main use is to name categories of items. For example, if you engrave with a long wand and the bugs on the floor stop moving, you can then call long wands something like "stop moving 1". (For the curious, this wand is either sleep or death.) If you use up an item like a scroll or potion, and its effect isn't totally obvious, you are automatically given the opportunity to name it. In ADOM, if the item wasn't automatically identified, there's no way to add it to your discoveries list, even if you know what it was. What's more, some items (like the scroll of amnesia) won't auto-identify even though they should.
Nethack has a friendlier inventory management system. When you want to drop multiple items, you can select them from your entire inventory, or only from items of certain types. In ADOM, you can drop all items of a specific type, but can only select from your whole inventory, which will often be much larger than it could ever be in Nethack (there are no bags in ADOM). Nethack's #adjust command is also very handy - it makes it easy to set things up so that in every game, you can use the same sequence of keys to apply your unicorn horn.
Nethack always allows you to do what you want. For example, you can throw arrows with your bare hands (though they won't do much damage), and eat unpaid food or read unpaid spellbooks (though there will be a charge), all things which ADOM forbids you to do. It is said that the (Nethack) Dev Team thinks of everything, and it does feel as though they have considered everything the player could possibly attempt to do and come up with a plausible game response to it.
ADOM has far more equipment destruction than Nethack. In my opinion,this is the single most annoying feature of ADOM - it is very frustrating to have your precious girdle of giant strength ripped to shreds by an exploding door trap, forcing you to abandon much of the equipment you are carrying before you can go on. In Nethack, some items are vulnerable to being destroyed by fire, cold and lightning, and there are many ways to lose equipment through carelessness (such as blowing up your bag of holding), but many types of items are pretty much indestructible, and anything kept in a container is 100% safe from destruction other than through player error.
Nethack has a guaranteed wand of wishing, which means that you never have to spend ages hunting for a particular item that you can't live without. In ADOM, several rare items are absolutely required to complete an ultimate ending, and since there are no guaranteed wishes, it is sometimes necessary to spend a long time searching for them.
Nethack has explore mode and wizard mode, and its source code is available, so if you get curious about any feature of the game, you can experiment or source dive. (Some would say that this point is in ADOM's favour, since it forces you to solve the puzzles the hard way.) Some hackers refuse to play ADOM on principle because it is not free software.
ADOM has a much more complex game world, with many different dungeons set in a wilderness. The plot of a typical game is also more involved; it is likely that your character will complete many side quests before finally stopping the forces of Chaos. Also, "ultimate endings" are available for those who have won the game in the normal way by closing the Chaos Gate. You can try to become an Avatar of Order or Balance, or if you like being evil, a Chaos God (but then you will eventually be vanquished by a Champion of Law), or an Ultimate Chaos God (in which case you will conquer the universe). In Nethack, the only way to win is to offer the Amulet of Yendor to your deity.
ADOM also does much better on useful NPCs. Nethack has a few types of friendly monster, including your quest leader, but most monsters are just there to be killed. ADOM has many more peaceful NPCs, some of whom are just flavour and don't do much, others of whom send you on quests or teach you skills.
ADOM offers a much wider choice of characters (ten races and twenty classes), and they are better differentiated than in Nethack, where most late-game characters can survive by simply whacking everything to death. In ADOM, it's a lot easier to survive if you can cast spells, but a combat wombat can still win the game. Different classes and races have different skills, some of which can be very useful.
Your alignment (lawful, neutral or chaotic) also makes much more difference in ADOM. (In ADOM, it is pretty clear that "lawful" means "good" and "chaotic" means "evil". In Nethack, things mostly work that way, but some oddities such as rangers being non-lawful are best explained by the AD&D meanings of "lawful" and "chaotic".) The only effects of alignment in Nethack are that different alignments receive different artifact weapons and that there are a few actions for which lawfuls are penalised and chaotics are rewarded. Also, your alignment will only change if you sacrifice on a noncoaligned altar while in bad standing with your god. In ADOM, your alignment is a measure of where you fall on the spectrum from extremely lawful to extremely chaotic. All sorts of actions can change your alignment, and can easily push you over the threshold between two alignments. Alignment affects NPCs' reactions to you; many NPCs don't like chaotics, but there are a couple who will only talk to you if you are chaotic.
ADOM is more challenging in the late game than Nethack. Nothing can weaken a typical advanced Nethack character with a full ascension kit. (This is less true in Slash'EM because of wands of draining. In Nethack, level-drain is sufficiently rare that you will almost always have regained the level before you are drained again.) If you have magic resistance, you are safe from the destroy armour spell, and if your stats are somehow reduced, a unicorn horn will restore them. Late-game Nethack characters can be killed by running out of hit points, or by deadly sickness, but even that is rare. In ADOM, highly advanced characters are more vulnerable to hit point damage than in Nethack. They are also subject to unnatural aging (potentially fatal to short-lived races) and to stat drain, which is not trivially fixable in ADOM.