In my opinion, Calyrex-Shadow is superior to Calyrex-Ice competitively, though like xx_Mythical said, it mostly depends on the kind of team you are running it on.
I'll start with Calyrex-Ice:
Calyrex-Ice is an amazing Pokemon under Trick Room, outslowing most Pokemon. It also has an amazing base 165 attack, great 100/150/130 bulk, and a great offensive ability in As One (which is basically Chilling Neigh + Unnerve). It also has arguably the best physical Ice move in the game in Glacial Lance, a 130 BP physical Ice move with no drawbacks outside of its relatively low PP. On top of that, Calyrex-IR have good coverage with Close Combat, High Horsepower, and Crunch, among others. Its lack of a reliable Psychic STAB is negligible because of how powerful it is (and because Psychic is usually a subpar offensive type anyway). Finally, Ice is one of the very best offensive types in the game (imo it's second only to Fire), and it have Swords Dance to boost its attack further (not to mention its bulk letting it use Weakness Policy effectively)
Here’s a set that will be amazing under Trick Room:
Calyrex-Ice @ Weakness Policy
Ability: As One (Glastrier)
EVs: 252 HP / 252 Atk / 4 Def
- Substitute / Swords Dance
- Glacial Lance
- High Horsepower
- Trick Room / Close Combat / Crunch
Under Trick Room, this thing is an absolute menace. It underspeeds just about everything, and most Pokemon that actually can hit it before getting completely destroyed (Yveltal, Marshadow, etc) often are completely helpless as they can’t do anything significant without super effective moves, but super effective moves activates Glastrier’s Weakness Policy. Not to mention the power of this thing while Dynamaxed. Max Knuckle + As One (Chilling Neigh) lets it snowball extremely quickly.
On the other hand, Calyrex-IR is extremely reliant on Trick Room and often becomes a liability outside of it. Many Pokemon can hit it hard (like Calyrex-SR or Zacian-Crowned), and they don’t have to worry about being hit first outside of Trick Room. This is compounded by the fact that its typing, Psychic/Ice, is absolutely horrendous, giving it a Stealth Rock weakness and a weakness to many common types like Dark and Fire. It is also setup fodder for Pokemon like Trick Room Dusk Mane Necrozma, which carries its own Weakness Policy to take advantage of High Horsepower. Because of this, Calyrex-IR is seldom used outside of Trick Room teams (and maybe defensive teams due to its good bulk while still having a good damage output). True, it is amazing under Trick Room, but otherwise it is not that great and can even become a liability.
Calyrex-Shadow, on the other hand, is a better Pokemon in… just about every other kind of team besides semi-stall or stall. In my opinion, while Calyrex-Ice is good, Calyrex-Shadow is absolutely phenomenal. I’ll explain why:
The ideal stat spread of an offensive Pokemon has an amazing attacking stat (obviously), a great speed stat, and good bulk (so… not Deoxys). With that in mind, it is logical to give the other attacking stat a lower number so more points can go to your attacking stat of choice. In addition, that Pokemon should have a good offensive typing and a good offensive ability. And… Calyrex-Shadow has just that - 165 SpA is amazing no matter which way you slice it, 150 Spe is incredibly fast, and 100/80/100 bulk is workable (but not too good, or it will be too broken). On top of that, Calyrex-SR’s ability, As One, has multiple purposes. The Unnerve part of it prevents the defender from eating a berry to heal or soften up a blow. But the most important is the Grim Neigh part, which boosts its SpA whenever it gets a kill. This, combined with Calyrex-SR’s blazing speed, allows it to snowball out of control quickly and easily. Finally, Ghost is one of the best types for neutral coverage, as it is only resisted by Dark and neglected by Normal (which, in Ubers, is not very common). It is also worth noting that the other Pokemon that have these traits, Zacian-Crowned, cannot hold an item and cannot Dynamax, yet it is still a top Pokemon. It even has the coverage it needs, between Draining Kiss, Leaf Storm/Energy Ball, Psychic/Psyshock, and Pollen Puff. And all that goes without mentioning Astral Barrage, a 120 BP special Ghost-type move that, again, has no drawbacks besides its low PP. It also has access to Nasty Plot, which allows it to function as a wallbreaker as well as a sweeper.
Calyrex-Shadow @ Life Orb
Ability: As One (Spectrier)
EVs: 252 SpA / 4 SpD / 252 Spe
- Nasty Plot
- Astral Barrage
- Draining Kiss / Leaf Storm / Pollen Puff
Arguably the best sweeper in the game. Astral Barrage is a nuke even if it’s not boosted at all, and Psyshock destroys any Blissey or Toxapex that attempts to wall this. When Dynamaxed, Psyshock is a key move as it becomes Max Mindstorm, which summons Psychic Terrain, which prevents Sucker Punch from being used, which is arguably Calyrex-Shadow’s biggest weakness (besides Shadow Sneak of course). For the final move, Draining Kiss can be used for a better matchup against Yveltal and have access to recovery (boosted Draining Kiss recovers a massive amount of HP against Dragon-types). On the other hand, Leaf Storm can be used for problematic Pokemon like Tyranitar (which easily sponges Draining Kiss thanks to its massive special bulk under sandstorm). Finally, Pollen Puff can be used for other Dark-types as well as some Grass-types, though it is not really recommended. Calyrex-SR often can sweep a team by just spamming attacking moves without even trying to Nasty Plot, as its phenomenal ability allows it to catch up easily. Its mere presence basically mandates Yveltal on just about any team, and it is nigh-unstoppable once Yveltal and Ditto are removed. There is actually talk of a suspect test about Calyrex-SR because of how good this Pokemon is.
Well, every Pokemon has weaknesses, and Calyrex-SR is no exception. However, counterplay is extremely limited, and I will not be surprised if this gets suspected. Calyrex-SR’s biggest weakness is arguably its lackluster bulk by Uber standards, as well as extreme weaknesses in Ghost and Dark. However, even with these things, counterplay is still not easy to come by. Defensive counterplay has SpD Yveltal, SpD Mandibuzz, and… well… that’s it. That’s seriously it. However, Tyranitar works for variants without Leaf Storm, and Grimmsnarl can take on non-Leaf Storm variants thanks to Prankster Light Screen. Even Yveltal is shaky at best because Sucker Punch fails with Psychic Terrain up. Offensive counterplay is a bit easier, with Pokemon like Giratina-O and Marshadow KO-ing it with Shadow Sneak, as well as faster Pokemon taking advantage of its bulk. However, with Calyrex-SR’s amazing speed not many (viable) Pokemon outspeed it, even if they put on a Choice Scarf.
In conclusion, I feel like Calyrex-Shadow is better than Calyrex-Ice. Sure, Calyrex-Ice is good, but Calyrex-Shadow is phenomenal.