Two online collectible card games that Kongregate introduced to me are Elements and Tyrant. While Elements has more grinding and is more vulnerable to perverse randomization, I find it a superior game design. One of its virtues is that it takes advantage of being a computerized card game, rather than calling for physical cards.
This is typical with exporting existing things to new media or material. I recall the early encyclopedias on CD, some of which probably even made good use of hyperlinking, but they were largely a data dump of text into something more compact than a meter-high stack of books. In our gaming world, you had arcade ports to home systems without changing the dynamics built around “insert 25 cents to continue.”
Elements has cards that you could not exist in a physical CCG. Some of them are possible with a sufficiently large pre-made set, but let me give you some examples.
The simplest additions are things that are possible but inconvenient with physical systems. This was the great benefit of moving RPGs to computers: many of them involved a lot of math. (The great downside: losing the actual role-playing in favor of that math.) In Elements, quanta (mana) persist between rounds and can accumulate to very large numbers. Quantum Towers yield three random quanta per round, so a stack of 10 towers would require rolling 30 12-sided dice per round. Pests devour one random quantum per round, the same process in reverse. Hit point losses also persist between rounds, and creatures can be subject to healing, damage, and permanent changes to hit point caps. That involves either a lot of tokens/paper or two computerized variables per creature. Other cards and abilities make temporary and permanent changes to attack damage. Maybe your physical card game has a convenient way to track changes to multiple numbers on each of up to 46 different creatures, to say nothing of other abilities they might gain or lose as well as status effects, but I like computers for that.
Then there are token creatures. Some games do this well, but they generally try to minimize tokens unless the developers are also selling those. Several Elements cards generate more creatures, such as Boneyards that generate Skeletons, Pharaohs that generate Scarabs, and nymphs that generate explosive gas vials. These come together fully in the relatively new card Mitosis. It takes away a creature’s current ability and lets it generate a copy of itself (with the original ability back) at its casting cost. Mirror Universe copies an existing creature (with any changes).
The next step up is generating cards not on the field. It would be inconvenient but not impossible to keep track of Mitosis-created copies of a rare card in Magic: The Gathering, although you’d need Magic’s rule that unsummoning/killing a token creature completely removes it from the game unless you have copies to put in your hand/graveyard. You would need a ridiculously good collection to use a Fallen Elf/Druid, Mutation, Fate Egg, or Shard of Serendipity, which all create random cards. A “mutant” creature is randomly any one from the game, with a random bonus to its status plus a random ability (Fallen Xs mutate creatures). Fate Egg transforms into a random creature. Shard of Serendipity gives you three random cards. There are conceivable ways to do this with physical cards, say having a fixed set of cards and some randomizers and a reserve of them and… but I like computers for that.
Then there are cards that transform into other cards. An unsummoned Mummy becomes a Pharaoh, and an unsummoned Skeleton becomes a random creature (like a Fate Egg). The Graboid and Phoenix also become other creatures when activated. You could do some of this with two-sided cards, although the “transforms into” creature is (sometimes) another card that could also be played.
Then there are cards that create more cards. Fractal fills your hand with copies of a creature and Nightmare fills your opponent’s. Mindgate gives you a copy of your opponent’s top card, which can lead to exciting resonance when both players have multiple Mindgates. Shard of Serendipity pulls three cards from nowhere. Maybe you keep several dozen copies of every card around in case people are playing with Fractal decks … but I like computers for that.
Elements also uses an AI for PvE. Tyrant has the computer play randomly. You can exploit the AI’s predictability, but it is doing better than flipping the top card of the deck.
Don’t get me wrong: sometimes it is a great thing to straight-up port the game to a different medium. There are many tabletop games that work much better on the computer because of the amount of bookkeeping, shuffling, etc. involved. But if you are going to make a computerized X from scratch, plan on the fact that computers are involved rather than physical X.