The top down, 2d Zeldas were very different games from the 3d Zelda's. While they all have the same elements, the elements that are the focus of the games are different. The main point of the 3d games, and why I like them so much, is their focus on level design, particularly in the dungeons, and puzzle solving. The focus of Zelda 1 and A Link to the Past is exploration and the finding of secrets. Like I said, all of those elements are present in each Zelda, but the 2d and 3d games emphasize them differently.
Before getting into those differences, I have to say that the graphics, sound, and music hold up very well for an early SNES game. A Link to the Past is pleasing on the eyes and ears, and is the source of many a classic Zelda theme.
The focus on exploration and secrets leads to A Link to the Past having the most packed and dense overworld of any Zelda game. There are secrets to find and goodies everywhere, as opposed to the empty Hyrule Fields or Great Seas of later games.
The puzzle solving, however, is very weak compared to later games. Usually I'd refer to the puzzles as just obstacles. The cleverness behind the inventive puzzles of the 3D Zelda games is not there.
Another area where the game falls short is the combat. It is not bad. It is just not as good as in other Zelda games. Link's swords are so small that you have to be ridiculously close to an enemy to hit him with a normal attack even with the master sword. This, combined with the inability to move or turn while using a normal attack, often makes the combat much more frustrating than it needs to be. I have much more fun with the combat in the original Zelda for that reason.
My problem, ultimately, is that I am not into what the game does best. Games all about collection were never my cup of tea, so I tend to focus on the other elements of those games. I know I'm missing the point about A Link to the Past when I complain so much about the combat and the relative quality of the puzzles, but those are the things I like and the things I have come to have high expectations for in Zelda games. While a great game for what it is, A Link to the Past is my second least favorite Zelda game after the horrible Zelda 2, and I believe it is overrated when compared to the later games in the series.