As an example, the card game of Uno looks like this: (Shared) Deck -> Hand -> Play. Your objective is to put all your cards in play. The speed of Deck -> Hand is normally zero and the speed of Hand -> Play is normally one per turn (you play an appropriate card onto the stack). The number cards have exactly one ability: if the opponent does not have a proper followup card, they force a random single-turn increase in their Deck->Hand. This is a powerful ability, but limited because the opponent has many ways to guard against it, and so the number cards are the weakest.
There are special cards (Skip, Reverse, Draw Two) with single abilities that are conceptually easy to understand, and since their effect cannot be prevented, they are generally more powerful than the "vanilla" number cards. They also happen to be number cards (i.e. they have a color and number that can cause extra drawing for the next player), so they are unequivocally better.
The most powerful cards are Wild and Wild Draw Four. These are good for a number of reasons: they break the restrictions your opponents' number cards place on your next card (you can play them any time), they have a more powerful version of the number card ability (because they have no number, only color, and thus the opponent is more restricted in his card play options), and a properly timed Wild Draw Four essentially causes the next player to lose the game because it breaches the usual Deck->Hand gap so badly. From a flavor perspective, the cards are very visually distinctive, and even powerful, as black is a striking departure from the primary colors of the number cards.
Uno is an obviously unbalanced game in the sense that the cards stack up into an obvious power order. It is balanced because everyone draws from the same set of cards, and because the more powerful cards are restricted to a fixed number per deck.
Poker is far simpler: all cards are restricted to one per deck, and there is a sharply defined power order and no opportunity to mess with the randomness of card distribution. Your strategic options all stem from the external, gambling aspect, as anyone who has ever tried to play poker without betting knows. You could just as easily be betting on random numbers from a theoretical perspective, although the flavor is much improved by using a standard deck of cards.
But now imagine the Poker TCG: you are allowed to use any non-joker cards you want in your deck, which only you draw from. If you're playing five-card draw poker, there are a very few possible options left. (You can't just come to the tournament with a normal deck, because you'll be struck drawing a pair of sevens while everybody else has an actual plan for victory.) The deck to beat is obviously Four of a Kind, which plays 52 aces, meaning it will beat everything except a straight/royal flush 100% of the time. So can you make a Straight Flush deck that will put one together over 50% of the time? Probably not, because your Poker TCG lacks any ability to modify the random values, and you have to put together a five-card combo with no room for extras. If each player gets to trade in some cards, the Royal Flush deck gets better. If each player can hold seven cards (as with seven-card stud), the Royal Flush deck gets a lot better. If there are cards dealt to you from an outside deck (as with Texas Hold-Em or blackjack), the Royal Flush deck takes a nosedive, because virtually 100% of the time it's better to have two aces than it is to have two high spades. Et cetera.
To complete our conceptual journey to TCGs, now imagine that the possible cards to choose from include not only the standard 52, but also cards that have all these modifications as described in the last paragraph, or cards that protect you from those modifications. For example, the Royal Flush deck would "run" (i.e. use) many copies of cards that let you draw extra cards, or cards that let you trade in cards, while a Four Aces deck would run cards that limit the number of cards drawn, or decrease the number of cards you can trade in (since a starting hand for Four Aces is the best hand it will ever get). However, it won't play many of these special cards, because each one threatens the consistency of the Four Aces strategy - what if you draw three tricky cards and two aces? Now a Royal Flush deck could beat you even if it doesn't get the whole thing set up! Unless, of course, the Flush deck's tricky cards allow 7 cards to be drawn instead of 5...
So the virtue of making your own deck of cards does not necessarily come from the interactions between the cards once they are in play, but rather the ability to alter the conditions under which the game is played. Of course, this can go too far; some of the most "innovative" ideas have ended in awful stalls where neither player's deck was prepared to play under the new rules and things slowly grind to a halt. Join me next time as I talk about the color pie.