After more than 20 years, I'm still trying to find that out.
I love the first LoZ, and I also like ST a lot. But, there are not much similarities between those games.
In terms of the impression the indivudual games gave me anyway.
Except that you are running around with a sword while dressed in green most of the time. But that's not much of a reson to like a game, is it? While the music is great thoughout the whole series, it's not the only reason for me to buy this stuff.
I think I just like the casual gaming feeling that I have, while playing these series.
Yes, this even applies to LoZ and AoL. You only have to use a d-pad and about three buttons man!
The beginning is easy, the end is pretty challenging but not next to impossible or anything.
And, there are no things in the game that you can't beat without knowledge from outside the game or anything.
(although walking through the wall in the second quest took me a year to discover...)
RPG games are so lenghty at times. While they have interesting stories, you need to fight many, many battles to get somewhere in terms of getting stronger. I prefer finding a Heart Container in a secret place over battling hundreds of enemies to gain a bunch of experience points and a few stat points if you are lucky. Then you've gone up one level, another 30 levels to go before you go the the final boss.
Games like Gran Turismo are fun when you are technically interested in tuning cars and when you paid attention at school. Games like first person shooters are fun if you are into that thing and they usually seem to be most fun playing online. Maybe they made it easier now, but some years ago, I would not know how to play a game on the Internet. Servers? Ping? I still don't know what all that means. And I'm not interested either.
You just jam a Zelda game in your console or handheld and play it.
Mario is good too, but way more frustrating and challenging. Like, it's really made to loose lives.... But you get 'em almost just as easy. Mario's lives are designed to last for a short time. Zelda games are more focussed on the long play instead of a short, timed stage you have to beat quickly. Of course, you can die, but otherwise it would not be exciting when you wouldn't have sweaty hands and a fast heartbeat when facing the final boss.
And it does have a story. I'm not much into Pac-Man, Pong, Bust-A-Move, Tetris and those games. Nice findings on Tetris, awesome inventions, very smart. But very boring too! I just can't play these things more than 10 minutes.
One more thing that made the games great was a world where you can walk around, instead of a level that you never see again unless you get a game over.... You could actually walk back and forth and even re-enter a dungeon. Awesome!
Casual gaming does the trick for me I think. In a very balanced video game series. Great music, good graphics, nice motions, complex stories and with some very relaxing gameplay combined with some peak moments to keep you on your toes.