Well, first of all I would just like to say that the original Link's Awakening is head and shoulders over the DX remake. They added color, which is fine, whatever. However they also took away features like pressing B to skip over useless text. Also, the photo booth thing is incredibly stupid and out of place for the style of the game.
That being said, I'm not sure if this is a fair comparison because as a group the oracle games are twice as big. Obviously they're better together. But as stand alone games, I think that I would go with Link's Awakening. It's got such a mysterious beautiful storyline. I remember pretty much sh**ing my pants as an 8 year old when I got to the face shrine. There are some pretty major plot ideas that make you question whether or not to even finish the game. LA is also a much harder game than the oracles, except for the final bosses. Over all though, I think that it's more fun to explore the land of LA and more rewarding to complete tasks. There aren't as many side quests, but keep in mind that this game is 17 years old. Back then, Zelda didn't have many. Personally, I think that LA is the best hand held Zelda ever made.
If you don't have the original, I would recommend playing it on an emulator. There's just no place for all the goofy nonsense that they added to the color version in the overall feel of the game.