After finishing Paper Mario 64 again my most scorching takeaway -- which I would probably need to replay TTYD to substantiate more because it's purely going off of memory from my last playthrough quite a few years ago -- was that I think Paper Mario 64's combat is arguably better designed than TTYD's despite having less hooks to it.
The biggest differentiator between both games is how Paper Mario 64's badge economy and offering is drastically different. The first game puts a cap on badges at 30 BP (TTYD caps it at 99), meaning it is extremely difficult to break the game and turns fairly crucial badges like Power Plus, Defense Plus, and Flower Saver into a massive investment that will have to come at the cost of some valuable skills that makes the most of it all. There's also far less in terms of unique skills and context sensitive badges. Most of all, the game has no badges that serve to buff Partners, which will be important in a bit.
All of that definitely sounds less "fun", you get to do less goofy builds, but it also means you have to consider so much when picking and choosing what to prioritize. There was a point after I bought the All or Nothing badge when I stopped for about 5 minutes to consider whether investing BP into it was more ideal than culling a skill to place the buff into another Power Plus instead. The resource loop of needing FP both for defense and offense, needing BP to offset FP cost but also needing BP to buff up damage/defense, is genuinely compelling. It makes combat encounters far more meaningful because there's a limit to how much you can bulk up, making enemies far more threatening and battles far more strategic. What surprised me in particular was how I actually got a Game Over in a random encounter, and some late game bosses are pretty notable difficulty spikes, including optional ones like Kent C. Koopa.
The partners meanwhile, despite being less individualized from the lack of partner badges and their own health, are probably the most understated element in terms of design. There's no hook to circumvent shortcomings of 64's gang through supplemental systems. Goombario is the strongest single target attacker but requires setup (and his Multibonk cap is bugged), Kooper has a solid debuff and an AOE that gets heavy usage during the late game, but he has no air coverage which makes him very suboptimal during mid game. Bombette is the strongest multi-target attacker in the early game but becomes progressively outclassed by Ultra Ranks from Chapter 5 onward and mainly sees use as a counterpick option. Parakarry has omnipresent coverage and power but is a monumental FP sink. Bow has the strongest resource-free single target damage and a full protective move, but has zero defensive penetration. Watt has really strong buffs/debuffs and defensive piercing but has no multitarget attacks. Sushie is like Parakarry but with more difficult execution, elemental advantages, and a buff move. Lakilester is comparatively weak as a late game party member but is an omnipresent low-risk/low-resource attacker with a nice defensive move. Despite having the most party members of any of the games, the game still encourages cycling through most of them as often as it can manage which adds another layer of strategy to everything. There's invariably a few weaker ones like Bow and Lakilester, but as previously said you're micromanaging resources a lot more in this game so using low-resource attacks when you can is often important.
By contrast, the thing I find about TTYD's motley crew is that some of them feel monumentally overcentralized because of badge buffing and are almost too individually strong in their own right; a few of them excel at too many things and have too many upsides for their archetype. Yoshi inherits Bow's low base defense penetration, but has Gulp as a two target defensive piercing attack. Upgrading Yoshi and loading up on badges turns him into a hydrogen bomb of a damage dealer, especially if you soften up enemies' defense or boost his power via moves like Power Lift. Vivian not only has Lakilester's omnipresent targeting but inflicts status effects and has an omnipresent multi-target defense piercing move, which is just insane. Finally Goombella inherits Goombario's single target dominance (without the bugged cap) and for good measure is also able to relinquish her turn to Mario, who is just always sitting on a smorgasbord of fuckery. All three of these practically demolish the need to think more strategically about which other partners to use.
I think TTYD has a lot of remarkable systems under the hood that you can stretch to its limits, and it's fun to do so, but I always felt this was less on account of clever application as opposed to raw brute forcing. In spite of all the little cool additions like super guards and the audience related mechanics (which as an aside further made combat pretty lopsided because building Star Power resources in PM64 was so much more difficult), it predominantly suffices as a fun exercise in how much time you can spend in order to watch numbers go haywire. There's a novelty in all of that, but after my first Danger Mario run I ultimately came away with this "emperor has no clothes" feeling about the game's combat as a whole, and this sense that vigilance decrement creeps up a bit too easily.