It's always tricky to find the right balance between how significant these games were at the time, and how well they hold up today. A Link to the Past is a game that did a lot and helped shape the series to what it became for years, but I would not recommend it to any one that isn't committed to playing every Zelda game. It established a lot of conventions, but it ends up having very little memorable of its own. Its successors would refine and and expand on all of its most interesting aspects.
To me, A Link to the Past is the game where most of the dungeons are kind of samey, items are only rarely encouraged to use, puzzles are relatively rare making the game more about simplistic combat and maze-navigation, and tons of dull, sword-fighting bosses. It also has a mostly empty world where timeless characters like "old man", "flute boy", sick boy" and "Lumberjack 1" and "Lumberjack 2" get as much development as the named characters. Probably great in the early 90s, but I didn't play it until well into the 2000s and it basically had very little to offer to me back then. I'm assuming that's why A Link Between Worlds deviated from a straight-remake, and attempted to spice things up with much improved level and puzzle design, and giving the world's inhabitants some more characterisation and personality.