It's really one game split into two. There's some new tracks in The Lost Age, but if you weren't a fan of the first OST, the second isn't any different.
The story continues in the sequel and rounds things out a bit more. If I had to pick between the two, The Lost Age is my favourite, but you can't have that without the first.
The story worked well for me as a kid, but every time I tried to replay it, I felt like there was WAY too much dialogue. Not that dialogue is a bad thing, but they were using way too many words to say something, and never seemed to get to the point.
But the soundtrack had a lot of memorable hits. I haven't played the game in more than a decade, but I can still remember a few of the tracks. The GBA itself didn't have the best sound production capabilities, but the compositions in Golden Sun are fantastic from what I remember.