I went through and looked up all the differences between the Naxxramases if people are curious.
Kel'Thuzad is certainly a big one but the fights that are going to be absurdly more difficult at 60 than 80 are Gothik and Four Horsemen.
There's a number of other changes to encounters 60 vs 80 that are pretty serious.
Anub'Rekhan: Taunt immune tank death is a wipe. Locust Swarm did 1,000 damage per stack at 60 (
https://classic.wowhead.com/spell=28786/locust-swarm) and 1,500 per stack at 80 (
https://wow.gamepedia.com/Anub%27Rek...-man_Abilities). 60 tanks would absolutely be one shot and needed to kite the boss, 80 tanks could just get healed through it.
Grand Widow Faerlina: Rain of Fire 2,000 at 60 4,000 at 80. HP quadrupled, so just a lot more tightly tuned. Also taunt immune.
Maexxna: This encounter is basically neutered at 80 and there's a number of reasons why. First HoTs can't be stacked at 60, only one druid can have regrowth up. Second, the raid wide stun is 10 seconds at 60
https://classic.wowhead.com/spell=29484/web-spray and 6 seconds at 80
https://www.wowhead.com/spell=54125/web-spray. Third Maexxna's base melee damage is 29,000 at 80 and 9,727 at 60 so she hits around 25% harder at 60 relative to hp pools. Fourth she's taunt immune at 60. So it's far more likely your tank dies at 60 and even if your tank dies at 80 you can taunt and keep going. Finally web wraps are put high up on the wall and take fall damage at 60.
Noth the Plaguebringer: 20 curses vs 8 on 25-man. Taunt immunity means blink actually does something.
Heigan the Unclean: In the same time frame there's 15 explosions in the 60 version and 11 explosions in the 80 version. So the dance is 36% faster. Also there's the tunnel teleport mechanic at 60 that just doesn't exist at 80. 80
https://www.youtube.com/watch?v=zuVX8x5dq3g start counting at 1:04 60
https://www.youtube.com/watch?v=wcHcHTAGGso start counting at 2:10. Also, taunt immune.
Loatheb's been talked about. He's also taunt immune at 60.
Patchwerk: Not too dissimilar actually. There's three hateful tank slots at 60 vs two at 80 and the 60 version hits roughly 25% harder and has more effective HP vs dps.
Grobbulus: Basically the same.
Gluth: Taunt immune, tank swaps are done through threat. Infected wound increases damage taken by 100 at 60 and 100 at 80, so stacks are about 400% more dangerous at 60.
Thaddius: Stalagg has a mana burn aura at 60. Looking at video
https://www.youtube.com/watch?v=hOeAmq3USPI There's a six second safe window for polarity at 80 (charge switches at 1:50, starts doing damage at 1:56). The window is four seconds at 60,
https://www.youtube.com/watch?v=9MQyZeI6QSk (3:16 polarity shifts, 3:20 starts doing damage) Thaddius, unlike many Naxxramas 60 bosses, is tauntable!
Razuvious: His shout instakills mana users at 60, but he doesn't have the dagger throw. Pretty similar, slightly more technical with LOS at 60.
Gothik: The tuning difference on this fight is fairly huge. A lot of guilds carefully CC tons of mobs at 60 to avoid being overwhelmed while it's a zergfest at 80. As a specific example, the arcane explosion the spectral trainees do does
https://wotlkdb.com/?spell=27989 550 damage at 80 and
https://classic.wowhead.com/spell=27...cane-explosion 550 damage at 60. So it hits roughly 400% harder at 60. Also the undead side is immune to magic at 60.
Four Horsemen: This fight might have the biggest difference in difficulty. First all the Horsemen are mobile and melee at 60. Second Horsemen marks last 75 seconds at 60 instead of 25 seconds at 80, the marks become lethal around mark 4 at 60 and mark 6 at 80. Third the Horsemen shield wall at 75%, 50% and 25% HP for 20 seconds at 60 making them nearly impossible to zerg down. So instead of a quick zerg on Korth'azz there's a long, drawn out sequence of group switches. Other funny tuning differences the void zones do less damage at 80 than 60.
From a video of a level 70 player doing the encounter.
And a level 80
Sapphiron and Kel'Thuzad have been talked about above.