Advance Wars 2 improves upon the original by adding new COs, maps and a lengthy campaign against the forces of Black Hole. At first, you could think it gets repetitive always fighting the same enemy, but now every other faction is playable during the story mode at some point which more than makes up for it.
Unlocking a CO for battle maps and versus mode is easier than ever too and it's no longer required to replay the main campaign over and over again. That's neat.
Mission design has largely improved as well. The first game's campaign felt almost like a tutorial for battle maps most of the time, but now only the first few missions are really like that. The downside is that some battles can get a little tedious near the end, often stretching past the 20 turn mark for the par time. The AI is also generally better and actually spends its funds.
On the topic of presentation, the game is pretty much identical to its predecessor. I'm almost certain that the sprites for units are the same, although the new COs have their own unique themes and the story is much better. It still has a lighthearted tone, but most of the main characters actually comment on the tragedy of war, except for Andy who's still a sociopath.
Overall, Advance Wars 2 seems like a standalone expansion for the original, but on closer inspection it's clear that the game represents an improvement on pretty much every single aspect that made the original great.