There's always a lot of discussion about this topic.
First of all, here's the actual difference in width:
Picture courtesy of http://www.oldvegaschips.com/1cardfaces.htm
To me, it comes down to just personal preference. But here are some typical comments about each size:
BRIDGE SIZE (smaller)
Bridge size is used for poker in almost all card rooms and casinos. Go figure, but that's the way it is.
Bridge cards are smaller so you can fit more of them in your hand -- especially useful for games like bridge or hearts where you have lots of cards per player. Of course, this makes no sense for Hold 'Em or stud or draw poker games.
It's easier to hold a deck in one hand when dealing, especially for people with smaller hands.
Some people say they are easier to shuffle, especially the riffle-shuffle used by dealers, where the cards are not lifted off the playing surface.
When picking up the muck pile or putting a deck back together after "washing" the cards (rubbing them all around on the table to mix them up), it is easier to square up the bridge cards because they are narrower and you can feel the direction easier. The poker cards are more square, with a smaller "aspect ratio."
POKER SIZE (wider)
Poker size is used for blackjack and other table games in almost all casinos, but not for poker.
This is the size most often seen/sold in stores, so many people have gotten used to them over the years.
Poker cards are the traditional size used by magicians.
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FINALLY, my opinion is that the
quality of cards you get (plastic cards like Kem/Copag vs. paper) is MUCH MORE important than the size.