This is going to make me sound like a total classic Paper Mario fanboy, but I don't think the new Paper Mario art style is universally better than the old one. I'm not really talking character design here - I think there's a happy medium between keeping the more original NPC designs while still making classic Mario species appear more "on model," kinda like what Mondo went into earlier in the thread. I'm taking more in general.
On it's own, the look is quite lovely. Mario and friends are these individual paper characters in a wider arts and crafts world, and they get a lot of mileage out of reinterpreting the Mario world in that art style. It even contextualizes the outline and flat colors, changes I don't specifically love but understand - it gives the characters this sharp, freshly-printed look. But it's a style that hits different beats than the more "storybook" look that TTYD and especially PM64 go for, where the paper makes me think more of a pop-up book. They are both their own things, despite Paper Mario (the character's) general design being pretty set in stone outside of colors and outlines and such. If a TTYD remake shifts the art style to be more like the modern games in that regard, I feel like something would be missing - still gorgeous, but the vibe would be off.