I'm definitely voting Katakuri here.
His base AP durability is already 5.2x and 4x higher than Nagato's base AP and Shinra Tensei AP respectively (22.4837704 Gigatons vs 4.3 Gigatons and 5.68 Gigatons), meaning that pretty much none of Nagato's regular attacks would do much of anything to Katakuri, and it becomes worse when he coats himself in Buso for defense.
When Katakuri uses his Devil Fruit, the AP of his attacks become 14x and 10.5x higher than Nagato's durability, which means that any single attack could oneshot him, momentarily taking him out of commission until he regenerates.
Katakuri's Advanced Kenbun would also allow dodge/see any attack that Nagato sends his way several seconds before he launches it out. This would be very hard for Nagato to deal with, as he has no meaningful speed amps to deal with it.
Katakuri can deal with Chibaku Tensei and Shinra Tensei pretty easily even if we ignore how his durability is higher than both of them (1.3x higher than Chibaku Tensei). Katakuri's body is made of Mochi, which was stated to be a
special Paramecia with
Logia qualities. Because of this, he'd be immune to attacks of this nature,
as his body would just reform, and since Katakuri has over a 13000x LS advantage, he'd be unbothered by this.
On the topic of LS though, Katakuri would simply
smother Nagato with Mochi, which counters Substitution Jutsu.
Katakuri can survive having his soul ripped via sheer willpower:
Resistance to Soul Manipulation via Willpower (Those with strong souls, which are homologous to shadows, resist the effects of Brook's soul manipulation)
...with Brook's soul manipulation being able to
pull the souls out from a horde of enemies. This is layered with Haki.
On top of this, even if Katakuri does get his soul ripped, he'd still survive. In One Piece, people have 2 souls. Their soul and
their shadow. We know that they are separate things, because not only does Brook literally say so, but it was also stated by Lola ("
when [shadows are] inserted inside a person with a soul..."). We know that individuals can live with just one and not the other. Individuals with souls but no shadows are able to
live full-length lives as long as they don't step out into the sun, and individuals with shadows but no souls are
able to do the same.
Whether Katakuri's soul gets ripped out or not, his shadow will still be there, and because of that, he'd still be able to fight.
All in all, I believe Katakuri wins here because of his vastly superior AP, Durability, and LS that would allow him to overwhelm and eventually incap Nagato. On top of this, his Advanced Kenbun would let him avoid getting hit by certain attacks, and his mochi body would allow him to not be effected of other attacks.
