Personally both are flawed heavily. In terms of anime and card game. I know as I've played both and watched both animes and I must admit at one point I felt both of them were very good, but now looking back at it with a fine tooth comb. I just realize as a game and a series both are simply lacking in great areas.
Let's start with Yu-Gi-Oh: Once upon a time the series was very good, it wasn't heavily about a card game but more about a young boy with his troubles. Who had an alter ego who punished evildoers with games of death (shadow games). This is where YGO was at it's best, not a money grabbing cashcow based on a card game but had a very unique way of showing the bond of people and a unique story which gripped the audience. Then Duel Monsters came along and it went into a card game anime, and for the most part it was pretty good, though it suffered from one problem and this game with the later series like GX and 5D's (which were good in their own ways too) the main character was the one doing all the work and winning all the time. Only losing when going through what I like to think as an emo stage. Also I noticed that they never really like women. I'm a guy so this might sound weird but I'm all for equality not one side gets everything and the other gets f**k all. Most of the women in YGO are useless (Anzu, Ruka, Kotori, Rei etc) and even the ones that show promise like Mai in the original or Asuka in GX to Aki and Rio in 5D's and Zexal respectively, are seen starting off strong and not doing anything afterwards. Mai went emo, Asuka was a damsel and that was it. Aki became a dripping fangirl who LOST HER POWERS! Which was the main part of her and Rio well she just doesn't get to do much as Yuma like Yusei, Judai and Yugi before him take the spotlight 90% of the time.
As a card game Yu-Gi-Oh started off a thing of beauty a basic card game that got us all excited, I played when the first booster pack Legend of Blue Eyes came out and stopped just at the end of 5D's. When it first came out a rare card was a RARE card when we saw a Mirror Force or a Heavy Storm it was on everyone's hit list to get they were really rare cards that people went out their ways to get to improve and expand on the deck of the ways of an anime. However, when the 5D's and Zexal era started the game went downhill it was heading down a rocky path with Chaos decks being introduced in GX but it went downhill and became too complex with Synchros and Exceed letting you summon monster's left right and center, traps and magic cards which have stupidly overpowered effects and in general takes away the support of the older stuff only showing stuff like Dark Hole and Monster Reborn back from the old era. Which to many players are frowned upon for being too OP. Synchro's had some ridiculous monsters like Goyo Guardian and the Ice Barrier synchros which had some of the most questionable effects and in Goyo's case attack power seen in any card. And Exceeds (XYZ) well the art of special summoning is too heavily seen now, making the game pointless unless you have a certain card. Also note what I mentioned about rare cards being a thing of beauty and everyone wanted one. Now everyone gets ones in trail decks and the once 50 dollar or pound card is now worth a stick of bubblegum. They claim this is to make it easier for newcomers into the game and keep balance but if you ask me it just made cards pointless as getting packs seems like a waste of money now.
Now onto Vanguard: The series was good in series 1 showing off characters and clans off equal and decent capability the main character wasn't a wrecking machine who could simply defeat anyone. Though sadly this went downhill in the later series as he becomes nearly unstoppable. However, unlike YGO they made the women characters of value here, though in season two Misaki is seen being the worst character on the team, so much so fans on Bushiroads official site stated they wanted Misaki to get booted off the team because she wasn't winning a lot. Bring back the problem with equality, another issue with the series is the most recent series has been very very poor. Series 1 balanced the cardfights and storyline very nicely giving the viewers something interesting to watch. Season 2 focused two heavily on the cardfights and as such it had little to no character development and no real surprises. Season 3 the current series is the polar opposite focusing on plot over the fights as parts are cut out or edited heavily. Unfortunately it still doesn't give you character development or a decent plot taking wayyy too long to get to the main plot which if you really think about it reminds me a lot of the 60's British show Captain Scarlett and the Mysterons. And if you look carefully at both I'm sure I'm not the only one who thinks this.
Now the cardgame as a whole, once again started off great. All clans were getting support (minus the exception of Nubatama) and they were all standing well against each other. At least this is what I would say in the Japanese game, in the English it is like it got put in a blender and it's guts are spilling out. Number 1 case packs ARE NOT RELEASED IN ORDER! As such clans are often forgotten about because we are stupidly trying to keep up with the Japanese game as opposed to playing it at a steady pace, which would have been better as the clans wouldn't be hopeless lost in a void (wahaha Season 2 & 3 reference). Number 2 case certain clans getting too much support, in season 1 barely any clan was as tough as another, but come season 2 and 3 this all changed. Season 2 completely wrote out Royal and Shadow Paladins as well as Kagero the clans that were huge favorites and replaced them with Aqua Force, Narukami and Gold Paladins. Clans that are now ruling the meta game especially with season 3's Narukami being so stupid that they can nuke an entire field in one go. This is also due to the fact of "The main character/villain plays it, that's what people love right?" syndrome hence why Gold Paladins dominated the English meta game because with the silly pack order apparently it goes 1, 2, 6 now not 1, 2, 3. We got extra sets and normal packs out earlier then they should have been. Plus we notice it is the main character decks that get the support.
Final case People keep saying this to me which I think is stupid. I hate the people who claim that certain clans no longer get support because they have too much support. The clans I like to put to attention are Nova Grappler (played by Kamuni in the series) and Oracle Think Tank (once played by Misaki). Nova Grappler are still even in the later sets getting support including a break ride in set 10 with other beast deity support and even getting a cross break ride in set 13 (at least that seems to be the case). Oracle on the other hand have had no support and won't get any more until Mystical Magus in series 3 because those genius people at Bushiroad *eyes roll* thought of making a new clan called Genesis which look like Oracle Think Tank, play like Oracle Think Tank and the units sound like Oracle Think Tank units. So if it sounds like a duck, looks like a duck and sounds like a duck it according to Bushiroad logic it is a lion. This is just a lame excuse to push yet another clan which was not needed to be introduced especially since OTT have had there support completely destroyed by pack order releases. And this implies for other clans like Shadow Paladins. Shadow Paladin were considered a top deck when they were first released in Japan and have just recently done it again with the new SP support in pack 12. However, when pack 4 their first pack came out in English we already had packs 6, 7 and extra set 3 out. Which gave use cards like Ezel, Spectral Duke Dragon and Vermillion. So the all powerful Phantom Blaster Dragon was really really weak when it was released due to previous cards having better effects due to limit break.
So in short due to Bushiroad's idiocy the game has been completely ruined. And in conclusion to this debate neither series or game have much to stand up on with there complexity issues and as such lost a great deal of appeal to many. Including a die hard card gamer like me. If you want a card game that is balanced I would say go for the new boy on the block by Bushiroad, Weiss Schwartz a game that has animes and games battling it out to see which is best. Showing series like Fairy Tale, Fate Zero, Persona 4, Sengoku Basara, Project Diva, Sword Art Online etc. All with great art work and no particular series being superior to another like Vanguard or have a silly mechanic like Synchros, XYZ, Breakrides etc from the others.
Hope will never die!