Four Swords Adventures is without a doubt a more impressive game than Four Swords.
Four Swords is kind of.....a mini-game (at least I think of it as such). It's a very small game, has very limited items, storyline, and really anything you think of when it comes to Zelda games.
Four Swords Adventures is more of a full fledged adventure, with 9 different levels and three different stages in each level. It has storyline, characters, items, heart containers, fairies, tingle, bosses, everything you'd find in a more traditional Zelda game.