Dice win hands down on this one. There's something almost magical about the click and rattle of dice as you prepare to roll them, and the feel of the cool plastic on your skin. Cards can't compete, even when laminated with a silky-smooth plastic. They just don't feel right, with their sharp edges and the frankly worrying expressions on the faces of the picture cards.
Again, an easy win for dice. There's such a wide variety available, almost any colour or pattern, from plain primals to polished gold, even a variety of shapes. And when you roll the dice, the patterns swirl with an almost hypnotic effect. Cards are mostly flat and boring, although there are a few more interesting packs on the market, but they don't move when you play them.
I'm just making this too easy for the dice camp here. Of course, dice aren't completely random due to the manufacturing process, but they're close enough for use in a game.
Playing cards aren't anywhere near as random, especially if the last card drawn is discarded, making a reducing deck of increasing probability. In other words, if the pack has half gone and no aces have yet turned up, the chance of drawing one is higher. This changes the dynamics of the game, and makes players more likely to take chances. System developers know this of course, and plan accordingly, but the flow of play is quite different between the two.
Judging just on the randomness factor, dice win again.
I have to admit, playing cards are much easier to store than dice. They all fit neatly together in a small stack, have their own box, and can be put in a draw or on a shelf with other flat items. Dice aren't great at stacking, unless you have all d6s they don't fit together neatly, and even then it's not easy to keep them under control.
On the other hand, playing cards are prone to wear, staining and becoming easily lost when separated from their pack mates. Also, once the GM's back is turned, someone will start building a tower with them, or start skimming them at other players. Ok, they can do this with dice, but it's much less common and potentially more harmful.
I'm going to call this one a draw, no pun intended.
If you're the kind of person who is bothered by this stuff, playing cards are more acceptable to be seen with than polyhedral dice. It seems society is more ready to accept a lone, hard-drinking gambler than an open-minded, intelligent and well balanced gamer. If you celebrate your geekery, and rightly so, this won't be a problem, and you'll whip them out for all to see. I have a small but varied collection of dice, many of which have never been rolled in anger, but look good on my desk.
If someone gives you a hard time about gaming, see here for some responses.
Value for Money
Comparing like for like, a basic single-colour set of polyhedral dice and a basic, linen finished plastic-coated pack of playing cards, you can get either for £2-3, so the price is pretty similar. The cards will wear out quicker of course, get dog-eared, stained, folded and curved. Some cheap dice lose their spots after a while, but you can always draw them back on. And of course, if you lose a single die you can buy another. Lose a playing card and that's the whole deck wrecked. (Although you can still build towers and skim them at each other.)
I think dice are more fun than cards. Dice feel better, sound better and look better than cards. They have interesting shapes and colours, and are overall little shiny, clicky crystals of joyful randomness.
Ok, so cards make better book marks, are easier to use to stop an item of furniture wobbling and can be made into a bikini, but these are just secondary usages.
In conclusion, dice are best, and judging by the small number of systems using cards, (I will admit my internet search of such games was brief) both developers and players agree.
If you'd like to join in with this discussion, point out any bias in this article, or just generally want to make a point, feel free to contact me.