[Melee Mewtwo]

I probably should have mentioned earlier that when I say Arceus I mean any of his forms. Sorry for the confusion. (Although, I will probably be using Ghostceus for a majority of my examples as I like him best at the moment.)

Mewtwo Calcs

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252 SpA Life Orb Mewtwo Fire Blast vs. 252 HP / 0 SpD Arceus-Ghost: 165-195 (37.16 - 43.91%) -- 0.39% chance to 2HKO after Stealth Rock

252 SpA Life Orb Mewtwo Psystrike vs. 252 HP / 200 Def Arceus-Ghost: 175-207 (39.41 - 46.62%) -- 25% chance to 2HKO after Stealth Rock

+1 252 SpA Life Orb Mewtwo Psystrike vs. 252 HP / 200 Def Arceus-Ghost: 263-309 (59.23 - 69.59%) -- guaranteed 2HKO

(I'm thinking of running 200 def as 56 speed let Ghostceus outrun SDRay and wipe it out with Ice Beam.)

So you have a solid Mewtwo counter without having to resort to checks like support Darkceus that have poor general usefulness.

Spikes immunity is a small advantage as not every team uses them and you still need to have 2 layers + SR before Arceus before Arceus starts to take more entry damage. (Unless you choose a SR resistant type in which case you need full layers) Being open to T Spikes is almost and advantage as it means you can throw out Arceus on a single layer so as to avoid any Toxics that would really cripple it. Plus, you can use the same support you use for Lugia and get better results out of Arceus.

Mixed bulk is something Lugia has going for it. However, that SR weakness still cripples it from being a very good switch-in to a majority of special attackers. Additionally, it is better to have a more reliable physical wall when it comes to building cores as Arceus + Chansey handles threats a lot better than Lugia + Chansey.

Special Calcs

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252 SpA Palkia Thunder vs. 252 HP / 80 SpD Lugia: 190-224 (45.67 - 53.84%) -- guaranteed 2HKO after Stealth Rock

252 SpA Palkia Surf vs. 252 HP / 80 SpD Lugia in rain: 169-199 (40.62 - 47.83%) -- guaranteed 2HKO after Stealth Rock

(So Lugia can't switch into ScarfKia under rain, either.)

252 SpA Soul Dew Latios Draco Meteor vs. 252 HP / 80 SpD Lugia: 222-262 (53.36 - 62.98%) -- guaranteed 2HKO

-2 252 SpA Soul Dew Latios Draco Meteor vs. 252 HP / 80 SpD Lugia: 111-132 (26.68 - 31.73%) -- possible 4HKO

Kabutops

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252+ Atk Life Orb Kabutops Stone Edge vs. 252 HP / 176+ Def Lugia: 273-322 (65.62 - 77.4%) -- 25% chance to OHKO after Stealth Rock

252+ Atk Life Orb Kabutops Waterfall vs. 252 HP / 176+ Def Lugia in rain: 164-192 (39.42 - 46.15%) -- 98.44% chance to 2HKO after Stealth Rock

(So Lugia can't safely switch into Kabutops)

Lugia suffers from Cube Syndrome, you are almost always better off running a defensive Arceus form with the exception of a few niche circumstances where Lugia's handful of minor advantages makes it a better pick.

I also agree that Speed Shuffler is a pretty crummy set. I was just trying to find a semi-legitimate niche for the poor guy which is why I made sure to mention his faults and include a video showcasing his justified OO status so as to not mislead readers. (it does get Roar as well as Whirlwind if you want to avoid any extra DTail hax)