The other answers are nice, but I wanted to add more context to them, because they're very much incomplete.
To be honest, this depends on your team a lot. Which one is better from them is a pretty relative thing, and without your team one can give an answer as a whole only. But still, I'll answer it with the whole metagame in mind.
Calyrex-Shadow is one of the best wallbreakers in Anything Goes, capable of mangling most common defensive Pokémon with ease thanks to its impressive firepower, highly spammable STAB move in Astral Barrage, Speed tier and great ability. With the ability to Dynamax in the equation, ShadowRex has prodigious wallbreaking potential.
ShadowRex's movepool is also pretty vast movepool, thus increasing its versatility. Choice Scarf, arguably its most common set, is one of the best revenge killers in the Anything Goes, and can deal a decent chunk of damage to almost everything which doesn't resist its STABs. It can also outspeed virtually every boosted threat in the meta, including Geomancy Xerneas, and can easily finish of weakened threats. It can also cripple its most common check - Yveltal - with Trick + Choice Scarf, as without Heavy-Duty Boots its switchins would be heavily limited, so you can take advantage of that pretty easily late-game. Life Orb and Choice Specs are one of the strongest wallbreakers and late-game sweepers in Anything Goes. Life Orb ShadowRex gets the OHKO on maximum invest specially defensive Yveltal, which is pretty rare right now, though. Choice Specs ShadowRex is the strongest unboosted offensive Pokémon in the meta, and is capable of OHKOing fast Zacian-C after Stealth Rock damage. Again, CalySpecs can also Trick the Specs to Yveltal, limiting its switchins a lot. Also, Specs and Scarf can viably run Aromatherapy, as they'll have ample of opportunities to use it because of the ample number of switches it forces. There's the SubSeed set, too, which can be a bit awkward for first-time players, as it trades in the immediate power behind other offensive sets for a slower-paced wallbreaking set. Its main goal is to use the combination of Substitute + Leech Seed to force normal checks such as Yveltal to use healing moves, in which case it can either use Taunt to prevent them from recovering and continue chipping them down with Astral Barrage + Nasty Plot, or set up with Nasty Plot to aim for a sweep from behind the Substitute. This set is also one of the best stallbreakers, as it can easily break stall with SubSeed + Taunt.
Teambuilding with Calyrex-Shadow isn't very difficult, too. It can synergise easily with other wallbreakers in the tier, like Marshadow and Zacian-Crowned, both of which can take care of ShadowRex's common checks (Yveltal, Tyranitar), and the latter in return can overpower the aforementioned Pokémons most common checks (Eternatus and Necrozma-DM respectively). It also doesn't need much support; the Yen core (Yveltal + Eternatus + Necrozma-DM) grants it a good shield against threats like offensive Yveltal.
But still, everything isn't well with Calyrex-Shadow. Yveltal, arguably the most common Pokémon in the tier, is ShadowRex's best check and is present on almost all balance builds. Getting past Yveltal isn't very easy for Calyrex, as non-Life Orb sets usually don't run Draining Kiss to Dynamax and deal some better damage. The double quadruple weakness against two common types in the meta is an issue, too. Also, it has almost zero bulk, so any super-effective or strong enough move can easily finish it if it fails to get the KO on anything. The issue of imposter-proofing is also pressing, as non-Choice sets running Draining Kiss (without an intact Sash if running one) can risk getting their Yveltal weakened, paving way for their ShadowRex to sweep in return. Other specially bulky walls, such as Ho-oh, which can check unboosted Calyrex can eat an Astral Barrage, and cripple it with sometime like Thunder Wave.
Overall, Calyrex-Shadow is undoubtedly one of the best Pokémon in the metagame. Its amazing qualities outweigh its weakness by far.
Calyrex-Ice is a dangerous Pokémon in the right condition, but that requires too much support. With the correct support, though, it can rip apart teams with great ease and be a terrifically amazing wallbreaker. It has the ability to beat its own checks, which is pretty rare and important, making it a pretty devastating tool in certain matchups.
The most viable Calyrex-Ice set is the SubSeed set. It is an effective wallbreaker with Substitute + Leech Seed due to its good bulk, great Attack, and very powerful STAB move in Glacial Lance, which can quickly dent Necrozma-DM along with Leech Seed chip damage. With this set, as I've mentioned above, it can also break stall and semistall pretty easily, the latter of which isn't a very rare site on the ladder also. While chipping Necrozma-DM, it can benefit Pokémon such as Zacian-C greatly as then the overall offensive pressure on the opposing team would be increased by a lot, especially when their main physical wall is being strained to check two threatening foes. On Balance and Bulky Offense builds, IceRex is an effective choice, because of the aforementioned reason and the ability to soft-check wallbreakers such as Zekrom, Eternatus, Groudon and Zygarde-C. For an overall description of Calyrex-Ice's wallbreaking potential, check my nom here. IceRex is also known for its Trick Room set, which is worth mentioning, but not its "best" set. It can be a fit on Hyper Offense teams as a sole Trick Room Pokémon, and if played well, it can very much put extreme pressure on the opposing teams (as showcased here).
Teambuilding with Calyrex-Ice is an experience worth gathering. You'll be using the Yen (Yveltal + Eternatus + Necrozma-DM) on generic balance builds, and if you're building with IceRex, in accordance to the set, Zacian-Crowned, Xerneas, Zekrom, Marshadow etc. are great offensive partners, and Ditto is a great overall team partner for speed control, and IceRex teams usually do lack that and it's important for a lot of teams.
But still, Calyrex-Ice is a pretty niche Pokémon as a whole, as if it's not very good but not bad either. It finds itself in a pretty awkward space in the tier. The attack and the bulk is amazing, but the speed is what lets it down. A slow Ice-type is a pretty risky option, because Zacian-Crowned, Marshadow, Necrozma-DM and Ho-oh are extremely common Pokémon in the tier. The added Psychic-type doesn't help it, too, as it increases its weakness to Yveltal, which can secure a KO with Foul Play. Glacial Lance, its main STAB move, also sports very low PP which can be stalled with Steel-types, which are pretty common in the meta. The Trick Room can also be stalled by Necrozma-DM + Yveltal, and status conditions such as Thunder Wave highly cripple it, lowering its overall potential drastically. The weakness to every hazard is expolitable and would be the first thing to come to the opposing trainer's mind if they see an IceRex on their screen.
Overall, Calyrex-Ice is a great Pokémon, but with some glaring weaknesses to common sights in the AG metagame, which can sour the usefulness of the amazing sets.
Now that we've'd a description of both the Calyrex formes, which one is better? I'll juxtapose the two closely in different areas and we'll, in the end, get our answer (as a whole, as you've not linked your team).
Calyrex-Shadow is very versatile. It has a lot of viable sets to choose from, and is a headache for almost every team to face. As I've mentioned, all of its sets have different functions and are pretty vast as a whole.
Calyrex-Ice, on the other hand, has sadly only two viable sets, and a few niche ones. SubSeed is its most viable set, and Trick Room is another one which is common. Other sets, such as Choice Band and Dual Dance have few glaring weaknesses and aren't really inclined for the Anything Goes metagame.
Because IceRex is a bit limited to a few sets, Calyrex-Shadow is the clear winner here.
Ability to beat own checks
I've mentioned this point for both Pokémon before, too. SubSeed (both Pokémon) can break their checks with relative ease, and with constant offensive pressure (Life Orb and Dynamax), both of them can blast through their checks. And with the metagame shifting to faster Yveltal sets, which are bit shaky Calyrex-Shadow checks, the latter can get even more chances to setup and sweep.
Overall, this is a tie as both Pokémon boast the ability to wear down/ beat their own checks.
Calyrex-Ice is a support-demanding Pokémon. It requires a lot of support because of its paltry Speed and defensive typing. Checks to threats such as Marshadow, Calyrex-Ice, Zacian-C and especially bulky Dragon Dance Necrozma-DM are appreciated, and not everything can be checked in a single team, especially if it's leaning towards offense, like a bulky offense build.
Calyrex-Shadow, though, pairs well with a lot of offensive threats in the metagame, including the ones mentioned in the above paragraph, and can pose a serious threat for offensive teams and balanced teams alike. It doesn't require a lot of defensive support as well, the Yen core is all it wants as a defensive backbone.
Overall, Calyrex-Shadow is the winner here as it requires lot less support when compared to IceRex.
Ease while teambuilding
A bit based on the support required point, but this is different. What all do you need to take care of while teambuilding with the two Calyrex's? As I've said twice before, the Yen core is all Calyrex-Shadow needs as a defensive core, and a lot of common offensive Pokémon can pair easily with it. Calyrex-Ice would put some pressure while teambuilding and playing, because of some lacking points which I have discussed above. The clear winner over here is Calyrex-Shadow, too.
Is it outclassed?
The big question. As a specially offensive Ghost-type, Calyrex-Shadow has dominance. The only other viable specially offensive Ghost-type is Lunala, which can partner with ShadowRex to form an offensive core, but is outclassed overall by ShadowRex because of the latter's better Speed and Special Attack stat, and offensively a better ability. As offensive Ghost-types, Marshadow and Calyrex-Shadow are the most viable options available, and actually you can't compare them. They both perform different roles, and as a whole Calyrex-Shadow is just a tad bit better, because if your Yveltal goes down, you're in a very difficult situation.
Calyrex-Ice also has almost no competition because offensive Ice-types are pretty rare in the metagame. The only other one is Kyurem-White (and sporadically Kyurem-Black) which is very niche. As an offensive Psychic-type, Calyrex-Ice is the leader, but IceRex scarcely uses Psychic-types moves so it would be unfair to judge it on that criteria.
In the end, both the Calyrex's aren't really outclassed in their own fields, so this is also a tie.
Now, we know which Calyrex is better in usual circumstances. Calyrex-Shadow is the clear winner here because of loads of reasons discussed above. Because you haven't shared your team, I can't give a very specific answer, but I hope this suffices as I've discussed almost every point here. And character limit reached. Hope it helped!