Two of the strongest duelists in all of Yu-Gi-Oh! are Yugi Muto and Joey Wheeler. Yugi is the King of Games, the best duelist of all time, and Joey is one of the few people in the world that has actually beaten him. Not bad!
While Yugi and Joey are both great duelists, they have very different decks and dueling strategies. Yugi works with spellcasters and the Dark Magician, while Joey uses warriors and Red-Eyes Black Dragon. But, which of the two has the superior deck when it comes down to it?
Yugi's boss monster, the Dark Magician, is better than Red-Eyes Black Dragon in terms of the show's mechanics. This is because Joey has virtually nothing in his deck to support one of his most powerful monsters, as opposed to the King of Games, who uses plenty of Dark Magician cards in his deck. Yugi knows how to support his boss monster, and Joey doesn't do anything to prop his up at all.
While Red-Eyes Black Dragon is Joey's boss monster, it isn't the best one in his deck. One of his real best monsters is Jinzo, a 6-star monster with the same attack points as Red-Eyes that has the unique ability to disable the use of all trap cards by both players.
This is a massively beneficial effect that can essentially render 1/3 of an opponent's deck useless, and Joey has this hugely powerful card in his deck. This alone gives him a leg up over Joey.
As previously noted, Yugi runs a lot more support for Dark Magician than Joey does for Red-Eyes. In fact, Yugi runs the entire archetype in his deck.
Yugi runs Dark Magician Girl among a variety of other cards that support his ace monster. He uses the Dark Magicians as the cornerstone of his deck. In comparison, Joey runs Red-Eyes Black Dragon in his deck with no other cards that help out his boss monster, which there is plenty of to take advantage of. Simply put, Joey doesn't use his cards to the best of their ability.
One of Joey's best traits when it comes to duels is that he's incredibly lucky. With that in mind, it makes sense that Joey runs quite a few cards that rely on his luck. Cards like Graceful Dice and Skull Dice strengthen his own monsters while weakening his opponent's, and he has plenty of other cards that can help him take control of a duel in a pinch. Most of the time, Joey can utilize these cards very well, which adds to his deck's power.
Yugi is the master of having very specific cards in his deck to defeat his opponents thanks to plot armor. One major example of this is a card called Ragnarok, which requires two Dark Magician monsters on the field that then wipe out the opponent's row of monsters if they remove all monsters from their hand, deck, and graveyard from the game. That's an awful effect (Raigeki exists), but, of course, Yugi had it in his deck right when he needed it.
Time Wizard is not a very good card (once again, Raigeki exists), but, in terms of the show, it is a huge part of Joey's deck, and it gets him out of several binds throughout the course of the show.
While Yugi does have a direct counter for this card in the form of Dark Sage, it can be used against other duelists and Yugi when Dark Magician isn't on the field. Wiping out an opponent's monster row is very beneficial in any duel.
One leg up that Yugi will always have over Joey are the Egyptian God cards in his deck. It's a hugely unfair advantage that Yugi has due to the fact that they're the strongest cards in existence—in terms of the anime, at least. Yugi simply wouldn't be able to use these in any fair fight against Joey, which gives him a great advantage over the underdog.
While only really used one time by Joey in the anime, Harpie's Feather Duster has been included in his deck before. This card wipes out an opponent's entire back row with no cost, and it is still used in the current day game in the competitive scene, only being limited in 2020 after years of being on the forbidden list. Obviously, this is a pretty solid card even in real life, making it a great boon to Joey's deck.
Joey doesn't have very good four-star or lower monsters. He has monsters like Panther Warrior which requires a tribute to declare an attack at 2000 attack points, and non-effect monsters like Baby Dragon with 1200 attack points. Yugi has an array of solid monsters with effects or better stats than Joey's picks, which is a huge part of any duel in its early stages.
However, using a star called Star Blaster, Joey can summon his strong monsters easily with only one tribute on the same turn that the weaker monster was summoned, which allows him to get monsters like Red-Eyes and Jinzo out on the field quickly. While this is helpful, it isn't enough. All-in-all, Yugi simply has a better deck than Joey on almost all accounts.
