The first ever SNK Vs. Capcom game came in the form of Card Fighters' Clash, a title which was an exclusive to SNK's Neo Geo Pocket Color console. The game involves your character walking around lots of different areas to collect cards and fight other card players. With over 300 cards collecting them all takes a long time. There are two versions of the game -one for SNK, one for Capcom, and to get every card you'll need both.
These games were not successful, at least in any country other than Japan. The problem was that both versions of the game were on unpopular hardware (the NGPC could never match up with Nintendo's Gameboy Color and Pokémon games) and so not many people got to ever play these games.