Vs. Physdef
252 Atk Protean Meowscarada Triple Axel (40 BP) (3 hits) vs. 244 HP / 252+ Def Gliscor: 432-516 (122.7 - 146.5%) -- guaranteed OHKO
252 Atk Meowscarada Triple Axel (40 BP) (3 hits) vs. 244 HP / 252+ Def Gliscor: 288-348 (81.8 - 98.8%) -- approx. 2HKO after Poison Heal
As you can see, Triple Axel is guaranteed to OHKO with Protean, no matter what, while non-Protean falls just a little short of the KO. This however, means that unless the opponent's Gliscor is somehow at full health the entire match, it would still be immensely threatened by Meow clicking Triple Axel, as the lack of Roost would make it hard for it to realistically be over 80% health at all times for it to have a chance to live 3 hits. The worst case scenario would be that Gliscor decides to use Tera Water the turn you click him and Toxic you, if you were to be Protean in this situation, you would be forced to switch out, as you just lost STAB on Flower Trick and Gliscor will take 35.7 - 42.6%, unlike the Overgrow variant that will still deal 53.4 - 63.6% all while still resisting Earthquake due to not losing its Grass typing previously.
While you may tell me: "well, just switch out and come back later", and you'd be right, but what if you can't? What if Meow is one of your last mons standings and you can't beat Gliscor or afford to have it be crippled by it? This is where Overgrow shines over Protean, as it allows you to stay longer on the field and be harder to take advantage of as your STABs always remain unchanged.
Vs.
252 Atk Protean Meowscarada Triple Axel (40 BP) (3 hits) vs. 88 HP / 0 Def Raging Bolt: 384-456 (92.9 - 110.4%) -- approx. 62.5% chance to OHKO
252 Atk Meowscarada Triple Axel (40 BP) (3 hits) vs. 88 HP / 0 Def Raging Bolt: 258-306 (62.4 - 74%) -- approx. 2HKO
Here, the Protean damage is much more noticeable, Triple Axel is almost guaranteed to KO a Raging Bolt from full, while Overgrow is nowhere near close the KO here. Protean is certainly more desirable in the situation that you NEED to kill or force the Raging Bolt out, but let's say, what if you whiff Triple Axel, or you fail the KO by very little?. Assuming a scenario where the Raging Bolt won't be able to click Draco Meteor and take it out without consequences, if you were to be Protean in this situation, you'd be at a severe disadvantage later, as you essentially lost your Electric resistance by getting rid of Grass, which means that you're in position to eat a Thunderclap the next turn if you decide to stay, for comparison:
252+ SpA Raging Bolt Thunderclap vs. 0 HP / 4 SpD Meowscarada: 87-103 (29.6 - 35.1%) -- 19.6% chance to 3HKO
252+ SpA Raging Bolt Thunderclap vs. 0 HP / 4 SpD Tera Dark Meowscarada: 175-207 (59.7 - 70.6%) -- guaranteed 2HKO (to simulate you losing your Grass typing)
In the case that you were Overgrow, as long as you still have over 35% HP left, you would still be in position to force out or kill Bolt than the Protean variant. While the damage difference is really noticeable, unless Bolt hasn't come out a single time in the entire match, it shouldn't be too complex to make it take chip damage beforehand
Vs.
252 Atk Meowscarada Triple Axel (40 BP) (3 hits) vs. 0 HP / 0 Def Enamorus: 312-372 (107.9 - 128.7%) -- guaranteed OHKO
You don't really need Protean to KO Enamorus, though one advantage that Protean does have in this interaction is that a STAB Triple Axel would still deal over 80% damage if the enemy panicked and attempted to live the hit by removing Enam's weakness to Ice with Tera Fairy for example, meaning that if she took any kind of chip beforehand (From Stealth Rock for example), it would still be KO'd regardless, though I'm not sure if this Tera typing is still used as much with the whole Tera Stellar Enamorus stuff going on, which doesn't change your base typing so it's irrelevant to discuss it.
Vs.
252 Atk Protean Meowscarada Triple Axel (40 BP) (3 hits) vs. 0 HP / 4 Def Serperior: 366-438 (125.7 - 150.5%) -- guaranteed OHKO
252 Atk Meowscarada Triple Axel (40 BP) (3 hits) vs. 0 HP / 4 Def Serperior: 246-294 (84.5 - 101%) -- approx. 6.3% chance to OHKO
It's obvious that a guaranteed OHKO>a very slight chance to OHKO, which to be fair, can be fixed with a single layer of Spikes, which bumps that 6.3% chance up to 81.3%. However, Triple Axel is not exactly the most reliable move, so in the chance that you whiff it, you'd have:
+2 252 SpA Serperior Leaf Storm vs. 0 HP / 4 SpD Meowscarada: 196-231 (66.8 - 78.8%) -- guaranteed 2HKO
+2 252 SpA Serperior Leaf Storm vs. 0 HP / 4 SpD Tera Dark Meowscarada: 393-463 (134.1 - 158%) -- guaranteed OHKO
An unboosted Leaf Storm does as much damage to a neutral Meowscarada as a +2 one does to Meow that remains Grass. Just for consistency, Overgrow has a better chance against Serp factoring misses there.