I'll add a few more points about Nethack vs ADOM. Disclaimer: although I am a veteran Nethacker, I have only won ADOM once. I am currently in an ADOM phase, but will probably go back to Slash'EM (a variant of Nethack) when a significantly different new version comes out. If this writeup seems unfairly biased towards Nethack, it's partly because SabreCat has already covered many of the areas in which ADOM is better.

Reasons why Nethack is better than ADOM:

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 amulet of life saving ripped to shreds by an exploding door trap when you were hoping to give it to the dying sage later. 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, anyone attempting to achieve an ultimate ending needs several rare items to complete a particular quest, and since there are no guaranteed wishes, it is often 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.

Reasons why ADOM is better than Nethack:

ADOM has a much more complex plot (as SabreCat mentioned), and it also has multiple endings. Once you've won 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 Nethack, the only effects of alignment 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 lawful and neutral or neutral and chaotic. 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.