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And vise versa

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Pokemon that can be caught in Alpha Sapphire, but not X:
All Gen 2, 3, 4, and 5 starters and their evolutions, Rattata, Raticate, Meowth, Persian, Koffing, Weezing, Porygon, Misdreavus, Unown, Stantler, Omanyte, Omastar, Raikou, Entei, Suicune, Slakoth, Vigoroth, Slaking, Baltoy, Claydol, Feebas, Milotic, Castform, Regirock, Regice, Registeel, Regigigas, Latias, Latios, Kyogre, Rayquaza, Deoxys, Kricketot, Kricketune, Cherubi, Cherrim, Buneary, Lopunny, Mismagius, Glameow, Purugly, Finneon, Lumineon, Uxie, Azelf, Mesprit, Dialga, Heatran, Giratina, Cresselia, Cottonee, Whimsicott, Darumaka, Darmanitan, Yamask, Cofagrigus, Frillish, Jellicent, Elgyem, Beheeyem, Bouffalant, Cobalion, Virizion, Terrakion, Tynamo, Eelektrik Eelektross, Lugia, Dialga, Zekrom, Thundurus, Landorus, and Kyurem.

Pokemon that can be caught in X, but not Alpha Sapphire:
All Gen 1 and 6 starters and their evolutions, all Gen 6 Pokemon (Excluding Yveltal, Spritzee, Aromatisse, Skrelp, and Dragalge.), Caterpie, Metapod, Butterfree, Spearow, Fearow, Ekans, Arbok, both genders of Nidoran, Nidorino, Nidorina, Nidoking, Nidoqueen, Poliwag, Poliwhirl, Poliwrath, Politoed, Bellsprout, Weepinbell, Victreebel, Farfetch'd, Shellder, Cloyster, Gastly, Haunter, Gengar, Exeggcute, Exeggutor, Cubone, Marowak, Lickitung, Kangaskhan, Mr. Mime, Scyther, Jynx, Tauros, Snorlax, Dratini, Dragonair, Dragonite, Sentret, Furret, Hoothoot, Noctowl, Ledyba, Ledian, Mareep, Flaaffy, Ampharos, Sudowoodo, Hoppip, Skiploom, Jumpluff, Yanma, Wooper, Quagsire, Dunsparce, Gligar, Snubbull, Granbull, Qwilfish, Scizor, Shuckle, Sneasel, Teddiursa, Ursaring, Swinub, Piloswine, Houndour, Houndoom, Smeargle, Smoochum, Miltank, Starly, Staravia, Staraptor, Bidoof, Bibarel, Burmy, Wormadam, Mothim, Combee, Vespiquen, Pachirisu, Buizel, Floatzel, Stunky, Skuntank, Bonsly, Mime Jr., Munchlax, Riolu, Lucario, Hippopotas, Hippowdon, Croagunk, Toxicroak, Carnivine, Snover, Abomasnow, Weavile, Lickilicky, Yanmega, Gliscor, Mamoswine, Rotom, Patrat, Watchog, Purrloin, Liepard, Pansear, Simisear, Pansage, Simisage, Panpour, Simipour, Woobat, Swoobat, Venipede, Whirlipede, Scolipede, Basculin, Sigilyph, Solosis, Duosion, Reuniclus, Ducklett, Swanna, Vanillite, Vanillish, Vanilluxe, Emolga, Karrablast, Escavalier, Foongus, Amoonguss, Ferroseed, Ferrothorn, Litwick, Lampent, Cryogonal, Shelmet, Accelgor, Stunfisk, Mienfoo, Mienshao, Golett, Golurk, Pawniard, Bisharp, Heatmor, Durant, Xerneas, Zygarde, Mewtwo, Articuno, Zapdos, and Moltres.

That should be it.

Notes: You must trade with X, Y, OR, or AS to get Porygon2 and Porygon-Z. In order to get Giratina in AS, you have to also have Palkia, which can only be obtained in OR. In order to get Landorus in AS, you have to also have Tornadus, which can only be obtained in OR. In order to get Kyurem, you you have to also have Reshiram, which can only be obtained in OR. You have to choose between Amura and Tyrunt in X, so one if always unobtainable without trading.

Sources: This, this, this, and this.

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I don't think it's possible to catch the starters or Castform.
@sumwun For the starters, Gens 1 and 6 are found in X and Y, while the others are found in ORAS. As for Castform, the Weather Institute in ORAS exists for a reason.
Those are gifts. The player never gets an opportunity to catch any of them.