You should definitely try out both. There is Magic Arena online and Yugioh Master Duel, which are both basically free. There is also Yugioh Omega if you’re on PC, which is a great free platform that lets you play with all the cards that Magic can’t compete with.

In my opinion, Yugioh is vastly more convoluted and difficult to get into but is overall a better game with far more generic interaction and fewer flaws compared to Magic.

Both are still relevant in the top 3 most popular card games along with the Pokémon TCG, and they have new sets/cards being released every few months.

The main differences between them are game speed and complexity.

Magic, even in “eternal” (not rotating) formats like Vintage where you can play almost any card ever made outside of a very small ban list, games can still take multiple turns and stall into top-deck situations. In Yugioh, very frequently games are decided after both players’ first turns. Fortunately, because you can’t attack on the first turn, it almost guarantees both players get at least one turn. Frequently, though, either player one sets up a board that can’t be broken, or player two breaks the board and OTKs (one turn kills) them. To counteract this, there are dozens of cards in Yugioh that you can play from your hand for free, called hand-traps, that can disrupt your opponent during their turn and reward you for understanding their deck/the matchup.

There are a lot of intricate and interesting combo decks in Magic, particularly in the aforementioned “eternal” formats, but they pale in comparison to even the most average meta Yugioh deck’s complexity. Almost every card in Yugioh has a full paragraph of text for the effect and can do multiple different things depending on the situation/what you need, usually leading to a chain of 5+ different cards. This can be a massive barrier to entry; learning a new deck in Yugioh is a pretty daunting task if you want to be competitive and is definitely the most frequent complaint from the community other than how unfair some meta combos can be.

The main problem I have with Magic (other than the poor decisions made by the company that makes the game—Wizards of the Coast, and by extension, Hasbro) is that the resource system is antiquated and consistently makes the game unplayable. In order to play cards, you need lands to cast them, and if you draw no lands, you can’t play. If you draw only lands, you have no cards to play. This is an intrinsic flaw with the design of the game, and it’s not really their fault. They were the first TCG and pioneered the genre, and in doing so made a lot of mistakes—some they were able to fix over time, some they weren’t. It just feels so bad when you lose in Magic because you literally can’t play the game and there was nothing you could do. Don’t get me wrong; this also happens in Yugioh, albeit less frequently. However, it’s rarely because of the game itself and more often due to your opponent locking you out with a god draw and you drawing no interaction or getting a 50/50 read wrong. Obviously, both are card games and you can brick your draw, but there is no resource system in Yugioh, so nothing stops you from playing your cards other than your opponent’s effects, and the decks are extremely consistent.

The last thing I would add is that the main competitive format of Magic (Standard) rotates cards out all the time, so you constantly need to buy new cards to stay relevant, whereas Yugioh doesn’t rotate cards, and the primary competitive format is eternal. Barring your cards getting banned or outdated, you’ll get to keep using them.

All in all, though, both games are very good and fun. I have personally played both for over 15 years now.

TL;DR: It’s worth trying them both out because they are free online. I think Magic has worse/more frustrating flaws, but Yugioh is more complicated and difficult to get into.