In total there are 7 Final Fight cards in the game, here's a brief guide to what each one does and how rare they are to obtain. These sprites were ripped by Bonzai.
Cody, based on his appearance in the original Final Fight, is not a rare card to get with it being a class C card, meaning it is easy to find. Cody has 500 hit points, and his back-up card is Haggar. Cody does not have any special abilities.
Damnd is a class B rarity, and he has a special ability called whistle which lets you get a randomly selected card from your deck.
Guy's card is ranked at class B so whilst not quite as common as Cody, it can still be gotten without much trouble. He has 500 hit points, and his special ability cancels counter attacks if the enemy has 1 or less characters. This is called the haya-gake.
With a class A rank, Haggar is the most difficult Final Fight card to get in the game. He's also the strongest Final Fight related card with a total of 700 hit points, and his back up characters can be Guy or Cody. He also has a special ability, the spinning lariat, will shuffle your deck after all your current characters have been returned to it.
Hugo and Poison's card is an action card. This lets you select one AC card from your deck, then the deck is shuffled. However, the card you selected will be at the top of the deck. This card is a class B.
Rolento is fairly useless, as he has few hit points. His back up can be Sodom or Damnd.
Sadly, Sodom hasn't faired well in his transfer to Card Fighters, and is a class D. He only has 400 hit points, and no special ability. His back up can be E. Honda, Rolento or Damnd.