Hmm, for me, what comes to mind when this question comes up other than Pokémon itself is stuff like Grandia and the Etrian Odyssey games. Grandia, because of stuff like the action gauge, and having to keep an eye on what the enemies/boss are doing, and what you should do in response. Are they charging up some devastating magic attack or skill, and should you use a critical attack yourself to cancel it? Is it safe to use a skill magic yourself, or would the boss be able to crit you and it's better to go for a normal attack or combo? It's all about paying attention to what's going on when, and knowing when's the right time to use the right kind of attack, when's the perfect time to go all out and when's the time to play defensive until there's a huge opening, you can cancel the boss and start piling on, etc.
Etrian Odyssey, on the other hand, because of just for one example stuff like the bind system, and having to learn which parts of enemies are responsible for what attacks and what kinds of binds you need to use to stop those attacks from happening (and of course, in the process of figuring that out, also learning how resistant those different body parts of the enemies each are to binds). And of course being cautious of how enemies can do that right back to you, so being aware of what kind of binds each of your party members is most hindered by and taking precautions as necessary to guard against that if you suspect a given enemy might be capable of using binds. And binds are just one of the game's systems, nevermind other kinds of ailments and all kinds of other stuff to consider. It all comes together really well.
I enjoy it, but calling Pokemon's battle system the best in the genre is way too much of a hot take for me, especially when Xenoblade Chronicles exist (that battle system was unlike anything I had ever experienced. Yes, I know it's not "traditional" turn-based, but given the cooldowns act like turns + freedom of movement and how much movement matters, it revitalized the genre for me). The only time it doesn't feel boring is when you're facing against another human opponent. And frankly unless you're playing Gen IV and V, you're definitely going to be mashing A when you battle against AI characters because there's zero emphasis from Game Freak on the subtle elements such as: teambuilding/diversity, strategy, movepool, and stats (IVs + EVs).
Eh, not the first time I've heard that comparison, but no, Xenoblade is an ARPG through and through. Cooldowns don't make it turn-based or act like turns in any way. Especially since they're not meant to function as the equivalent of turns, but if anything meant to be the equivalent of PP in Pokémon or MP/SP/whatever you want to call it in other RPGs since Xenoblade doesn't have that either. The point of cooldowns is to keep you from being able to just spam stuff over and over again, which can be seen in particular by what's chosen to have the largest cooldowns, such as Sharla's healing arts (to such an extent that Sharla's Talent Art is a global cooldown of her other Arts you have to keep on top of), Shulk's more powerful Monado Arts, etc. And just how there's such variation in cooldowns in general between different Arts, that doesn't lend to game acting much like turns at all.
Cooldowns in Xenoblade, like other RPGs that use cooldown systems, are there as an alternative to mana points and the like to balance different tiers of skills, that's all, so I can't really consider that.
Edit:
Persona 5 has the best turn based battle system ever made imo
Now this is a "hell no" to me personally. Because I don't know much about the SMT games, so I can't speak to much to them and could easily be missing something fundamental when people bring them up as I really have no clue how exactly they differ from the Persona games in terms of combat, but as someone who is familiar with Persona 4 and 5 I definitely can't say they have a better battle system than Pokémon. Stuff like Persona 4 and Persona 5, especially against the mob enemies, come down to elemental weaknesses even more so than Pokémon. Either you know what they're weak to, and kill them super quick by being able to exploit that, since not only does exploiting elemental weaknesses in Persona games do more damage like in Pokémon, but it awards you with an extra turn so you can do even more damage and repeat or buff/heal if you need to instead. Only difference is, it's not necessarily obvious what type of stuff enemies are weak to, especially at first, and part of the trick is figuring that stuff out before they exploit your own teammates weaknesses. But it's the same rock-paper-scissors stuff driving those encounters.
And as for bosses, who tend not to really have elemental weaknesses as such, the pattern there is buff your team's stats, debuff the boss's, then just use your strongest attacks possible, heal as necessary and reappy buffs/debuffs as necessary, repeat until boss is defeated. The same exact strategies that can be used in Pokémon. The key difference being that, in the main game, you rarely need to resort to stuff like the equivalents of Matarukaja and Marakukaja in Pokémon but the equivalents of stuff like Swords Dance, Nasty Plot, Quiver Dance, Shell Smash are all there. And of course just using your most powerful attacks whenever possible or otherwise exploiting elemental weaknesses is standard fair in Pokémon.
So SMT is something I can easily let slide, especially since I don't know much about the series and its intricacies, but Persona definitely doesn't have more depth than Pokémon, that's for sure. Especially since Pokémon not only has the same focus on weaknesses and strong attacks, buffs and debuffs and the like as Persona, not only its own status ailments which are also a huge deal (especially stuff like Burn due to lowering the Attack stat, Paralysis lowering speed, stuff like that), but it also has stuff like Weather and Terrain that Persona doesn't really have an equivalent to off the top of my head. Stuff like Psychic Terrain, which prevents priority attacks from being used while its in effect for instance. And then you have stuff like Trick Room, which completely reverses turn order and has teams entirely built around that. Stuff like that.
And that ain't even touching on the concept of Hold Items in Pokémon, which is the closest thing Pokémon has to armor and equipment, but instead of offering stat boosts (though some items have a stat-boost effect, like Life Orb, Choice Items, etc), they can have all kinds of other weird effects, like the Red Card forcing the first Pokémon that makes direct contact to be swapped out with a random Pokémon, the Eject Button which is pretty much the opposite situation (let's you get a switch if you're hit with an attack), Rocky Helment (does chip damage to any Pokémon that makes direct damage and that direct damage can easily add up, let me say that much), Weakness Policy (doubles attack and special attack if hit by a super-effective move), berries which restore half your health when you're in critical HP, and all kinds of other stuff, with part of the depth coming form how there are so many possibilities but yet you can only have one hold item on each Pokémon at a given time meaning you have to choose carefully which item you want to give each of your Pokémon and think very carefully about which item each of the opponent's Pokémon has equipped, as it very easily could be something that makes it faster than normal like a Choice Scarf, something that makes it hit harder than normal like Choice Band/Specs something that's guaranteed to let it survive one attack like Focus Sash something that can power it up if you use the wrong move and it survives like a Weakness Policy, or something else, and each of those items potentially demanding a different course of action depending on which one's being held (like using a Priority move or even faster attacker to deal with something holding a Choice Scarf, but using a multi-hit attack or counting on weather damage at the end of a turn to help deal with a Focus Sash).
Now, you might not need to use those systems in Pokémon, but to be fair, you can get away with not using a lot of stuff in Persona as well, even on the higher difficulties, and hardly ever need to min-max your Personas or go for the strongest ones possible, or anything like that possible either. That being the case, I really don't get what Persona's battle system has on Pokémon's.