ALttP is a fantastic game in its own right, establishing the basic formula that most Zelda games would follow for years to come, a great feeling of adventure and overall just a really solid title, but Link's Awakening takes that and adds something that will also be important for the series moving forward, its charm. The former made the foundation and latter gave that foundation its magic.
In terms of dungeons, while ALttP has the better set of them mechanically and design wise, LA only picking up its complexity and design until the last 3 dungeons, LA manages to give all of them a more distinct feel thanks to the music, despite being on a less powerful handheld than the home console entry, it sees fit to give every dungeon its own music, tracks like the Face Shrine given a tonal shift to match the story up to that point, the point driven far more home with the remake, still the original deserves all the credit for its initial inclusion. I will also give credit to the Thieves Den in ALttP, one of the dungeons that manages to tell a small story within it to give it a better sense of identity.
Music is special in the Zelda series and is something that on the whole LA manages to do better than ALttP, its tunes may not be as reused as the latter, but it doesn't take away from how memorable they are, little changes to even the classic overworld tune gives it an edge for me, the incredible Ballad of the Wind Fish is a fitting motif for a lot of key scenes with Marin, the inclusion of various songs that one can learn with the Ocarina give a greater sense of charm to the game, is a far grander soundtrack overall compared to ALttP, both have really iconic tracks, but LA delivers more of them.
The way that you get attached to the Island in LA is also worth of praise, thanks to the naturally paced trading sequence, while its ultimate reward is entirely optional, you still need to do most of it to complete the game, this simple concept makes it so you get more personal with most of the residents, you get to know them, their relationships, making you care more about what happens to them, the land of Hyrule may feel much grander and epic in ALttP, but one seeking a more personal journey and attachment to the characters in the world, is something that Link's Awakening delivers much better.
The story is also quite good in LA, while I'll always enjoy the classic tale of Zelda, Link and Ganon, there is something endearing about more out there stories like the one presented here and Majora's Mask. Its twist and ending, while something I knew even before actually finishing the game, still hits hard with a really great sequences. ALttP also has great sequences, the opening of the game, the Dark World itself, and Aghanim to name a few.
In the end both are games that I highly enjoy, but there is a greater sense of charm and attachment that I feel with Link's Awakening due to the reasons I mentioned, and taking out of a contest between the two, over 20 years after its release, LA is still a kind of game with a setting and ideas that haven't been replicated again within the series.
