Let's get back to the basics. Wait! The basics have been spruced up a few notches!
First off, choosing 'Final Fantasy' at the starting screen will prompt a remake of the original game to begin. Nothing has changed in terms of the storyline from past games. The Dawn of Souls version still has the classic, (and very nostalgic) flow. The biggest difference that you see from the start is the amazing graphics upgrade. While it is still 2D, the maps are still quite stunning, and the characters look much more at home in the 21st century.
The characters of the original are all generic. You choose your characters at the very beginning of the game by selecting the classes that you want. You could have a full team of Black Mages or a mix of fighters and wizards. (By the way, "fighter" is now called "warrior".) The characters themselves don't contribute a lot to the storyline, save for the fighting, but that's what generic characters do, and again, the classic feeling is just right.
The battle system is also the same, (with only minor, apparent changes since the first version). You encounter regular monsters randomly and select which actions for your characters to perform. As always, this system is perfect, as it is for every other Final Fantasy game.
Lastly for the first game, there are new bonus dungeons exclusive to the new generation. There are four "Soul of Chaos" dungeons which become available during the flow of the game. Each of these dungeons has powerful enemies and randomly generated floor order. Generally, at the end of each, (though this happens in the middle in some of the dungeons as well) you have a choice between which boss you face. Every boss in the Soul of Chaos dungeons are cameos from the other games in the series, and as these are bonus dungeons, many of them are more powerful than the storyline's final boss, providing a new and very exciting challenge to all players.
Now for Final Fantasy II. This game has generally the same obvious change as Final Fantasy I. The graphics are updated in the same way, bringing the game a little bit more to life.
The characters of the second game are not generic this time. They now have their own individual names, appearances, and a touch of personalities. Now, they're still not as deep as the later games in the series, but it still works out great.
There are also apparent changes in battle too, though, if you're a younger player like I am, these won't be noticed. Most of these changes are in the leveling system, taking quite a bit of pressure out of the stat-gaining. (No more stat-loss.)
As for a bonus dungeon, yes, this game has that too. After you complete the main storyline, you can use a new save file for a previously unavailable area. I won't go into any spoilers, but rather than the main four characters of the main storyline, this dungeon stars a number of men who, erm, left the main story during the game, and takes place in synchronization with the ending of the original story, but in a very, very far-off place (hopefully).
So in the end, this is really an amazingly well done remake of Final Fantasy's original roots. If you're feeling nostalgic, but can't get your hands on the Nintendo copy (or the system to play it on) this is the best alternative. I tell you, there really is nothing like the great, simpler feeling of these two remakes compared to any other recent game today.