The main advantages of nighthaunt allegiance over a nighthaunt-heavy LoN army are:
1. Formations. Nighthaunts have some decent ones, I like the shroudguard, chainguard, and deathriders in particular. As of the core rule faq, to take any of tbese in a LoN list, youd have to pay for the entire formation out of your ally points, including for units that you otherwise could have fielded as a normal part of your army, which essentially blocks LiN armies from accessing nighthaunt battalions at all.
2. Deep strike. Nighthaunt can deploy half their units underground, and then put them on the table anywhere more than 9" from the enemy. And thats any unit, not just summonables. Even LoNight doesn't have that kind of deployment flexibility.
3. Alternative battleline. Chainrasps aren't bad, but there's a lot to be said for battleline grimghasts, hexwraiths, or spirit hosts, especially at higher points values where you need 3 or 4 battleline units.
On the other hand, LoN listd have necromancers (vanhels is great on grimghasts), vamp lords (nighthaunt can ally in soulblight, but LoN gives them better spells), monsters, gravesite healing, etc. Could go either way, really.