I personally loved Dark Dawn. I have played the original, and I still feel that DD is slightly better than it. I can't speak for The Lost Age, as I've never gotten the chance to play it (darn you, US virtual console!) But I can say with confidence that I enjoyed DD more than the original (though the original was very good, too). Reasons? Well, here you go for whoever is interested.
1: I didn't like how if you made two characters attack an enemy and one of them killed it, the other wouldn't do anything with their turn. That annoyed me quite a bit. I believe this problem was fixed in DD.
2: I didn't really feel like I accomplished anything in the original. At the end of it all, I just wondered what It was I was doing. I remember saving a village from being flooded, and protecting people on a boat. But at the end of the day, did Isaac and crew really accomplish anything substantial? I understand that's what the sequel is for, but as I mentioned, I never played it. So GS 1 is how the story ended for me. DD, while being somewhat of a big side quest, actually made me feel like I was responsible for what happened and really made me want to save the world. It was the story of Matthew stepping up to be a leader and fix the mess he helped cause. It was a cool story to me. That, and I liked DD's characters more than the original (though they were cool too).
3: The game felt longer to me. I'm not sure if it is or not, but it took me much longer to beat DD than the original. In fact, the original felt very short, making me want more. While DD left me feeling somewhat accomplished, but ended up teasing me with that cliffhanger at the end. If not for the cliffhanger, I'd say DD was a perfect length. Not too long, not too short. The cliffhanger made the adventure seem unfinished, so I can't really say that the game ended there. I can't wait to finish the full DD story in the next game.
4: I don't really mind when a game is easy, in fact, difficulty doesn't bother me much in games. If a game is super easy, it won't ruin my experience as I look for other things in video games than just difficulty. That said, the original was SUPER easy. I don't remember dying once, I beat all the bosses like nothing, and didn't even need to use one summon. I was way overpowered, I think. Nothing, not even the last boss could stop me. With DD, while also not a super hard game, It's difficulty never felt too easy or too hard. I also remember needing to use summons and having a hard time with the last boss. It wasn't a hard game, but I feel it was slightly harder than the original. Not by much, but a little.
5: Here is where I'd put minor things like "character designs", "music" and things of that nature. I prefer almost everything in Dark Dawn to the original. This is barely making my list, as I feel the original was just as strong as DD with these things, but I just happen to like one slightly more than the other.
And there you have it. I could go on, but I don't want to. Both GS and DD are amazing games, and I'll probably replay them both pretty soon (after I beat Phantasy Star IV). I know that I'm strange for preferring DD to the original, but I gave my reasons. Again, both great games, I just like one slightly more than the other.