Every time I play a complex board game, I think about crafting an organiser tray for all the game pieces. This imagined tray would have compartments for cards of varying sizes, tokens, dice, and so on, for several player characters, to help me manage and preserve the state of an ongoing game. A lot of board games, like Zombicide, Mansions of Madness, Fallout, Skyrim, Descent, have a lot of data to track. The way a game chooses to help the user track that data has implications on user experience and the identity of the game.
A token is one of the simplest assets in a board game. It represents a thing or an event or a condition in the game world. If you possess a token, then you possess the thing it represents. When you lose the token, you have lost the thing. It's a simple binary toggle, it's either On or Off.
Some clever designs grant tokens extra abilities. Maybe you get a token representing damage with one side facing up, but once you taken further damage you flip the token so that it represents a permanent injury.
Other tokens are entirely dual-purpose. One side represents a door that can be opened, the other side prepresents fog that can be lifted. Similar concepts, but unique enough to govern when one side is used over the other.
Tokens are nice because they're small, and they save players from having to take notes about the changing status of either the game board or their character.
They're also a great visual reminder of the game state. How much gold have you collected? How much health have you got left? Is this room lit or in darkness? Is the door open or closed? Just look at the tokens.
The limitation of tokens is that they're usually physically small. That means they're easy to lose, or to scatter all over the floor by accident.
It's also hard to include metadata on a token. Players must learn what each token represents. That's easy when a heart token represents health and gold tokens reperesent gold. It's not as easy when a green mist token represents the camouflaged condition, or a blue flare represents an active sprite, or a fireball represents the fireball spell with no reminder of how you cast it or how many dice you roll when you do. For all their convenience, tokens can end up obfuscating information that's meant to be very obvio us.
Too many tokens at play can also overload a player's ability to "read" the state of the game. You just start to miss the trees for the forest.
Cards are basically perfect, at least at first glance. As with all game assets, though, there's always a trade-off.
They're small and easy to carry around. But that also means there's limited space on them, which means you must choose your graphics and words carefully or else print everything so tiny that they become inaccessible.
They're modular, meaning a player can be take one card without having to taking another. They can be coded into groups either by their backs or by some graphical notation on their faces. Then again, they take up a lot of space on the table or in the player's hands. To conveniently see all of the cards you have at the same time, you need a lot of table space.
They're also stackable, which means you can essentially collapse them so they have a small footprint when they're not being used. However, when you stack them you necessarily lose sight of some of them or some of the data on them. There's also a point at which a stack of cards becomes unwieldy. 30 or even 100 cards in a deck is one thing, but try stacking 300 cards on top of one another during an exciting game and see how long it stays tidy.
Cards can (and usually do) serve as tokens with rules included. By possessing a card that represents a thing in the game world, you demonstrate that you have possession of the imaginary thing. The card also provides stats or rules for the thing that it represents.
Especially common for tabletop roleplaying games, but usually included along with every board game, are books. The rule book is the ultimate source material for practically any game. It literally defines the game, along with everything used to play the game. In theory, you can play any board game as long as you have its rule book, even without the game assets. In practise, few rule books provide full descriptions of literally everything in the game box, but assume for now that a rule book exists with all the information you need to implement a game.
With a book of rules and the computational power of a human brain, you don't need extra assets to play a game. Instead of drawing and holding a card to represent a thing or a spell or a condition, you could just take mental note of it, or write it down. Instead of taking a token as an indicator of something important, you can just remember it. If you can't remember the details of a complex rule associated with something your character has acquired, you can just look it up in the rule book.
A random table in a book is essentially the source code for a deck of cards. Instead of drawing a card from a deck, you roll a die, find the row that matches the number, and read the description.
I love a good deck of cards and find them useful for all manner of games, but it doesn't get any better than a good rule book. Then again, as with all the other solutions for conveying game information to players, a book also has some issues.
A book can serve as the complete documentation of a game system, but that in itself can make information difficult to locate. Games like Pathfinder 2 and Tales of the Valiant and Warhammer 40,000 publish some very hefty game books, and I use them weekly. However, the publishers of those books also release game master screens, cheatsheets, and decks of cards, and I jump at the chance to supplement the rule book with anything that provides quick reference.
Books don't tend to be modular, either. If you only need 3 or 4 pages from a book of 200 pages, there's no easy way to grab just the ones you need for a game, the way you can with a deck of cards.
Depending on your game's audience, a book also may not feel like a game. To a roleplayer or wargamer, sitting or standing at a table armed with several source books feels pretty natural. To someone just graduating from a lifetime of Monopoly though, or even a roleplayer or wargamer in the mood for a board game, spending 15 minutes at a time referencing a tome of rules instead of drawing a card can feel out of place.
There's no secret formula for the best form of any given game asset. Mansions of Madness uses a lot of cards, and it's definitely challenging to keep track of everything you get dealt during a game. Horror and Damage cards could easily have been tokens, with a dice roll on a random table (or a button in the app, in 2nd Edition) determining what effect the token has on your character. Then again, the game uses a lot of tokens already.
These are the kinds of choices a game designer must make. There are many ways to achieve the same technical result, and which one gets used is a matter of design, production, and player experience.