They've gotten facelifts however, and now feature 16-bit era graphics and CD quality sound and music. It's a tough call whether to say the new graphics are good or not. They certainly don't stand up to the graphics in Final Fantasy IV - VI, but you must remember that these remakes were originally made for the Wonderswan (a portable system that never saw the light of day in America, and didn't really do great in Japan either). So while the graphics could have been considerably better for a PSX game, we'll all understand if they didn't spend the time and money remaking all the art a second time.
The fact that they could have been better aside, they are certainly an upgrade from the 8-bit graphics of the original, especially the battles. The games also contain the obligatory new FMVs you can find in any Square remake. There are no ending FMVs this time however, just a quickie at the start. I do have one real complaint to make in the art department though, and it involves the monster sprites in Final Fantasy II. For the most part, in Final Fantasy I, Square used the original monster art; they just juiced it up with more colors. For some reason, however, they chose to rework the monster art from scratch in Final Fantasy II. Almost all the monsters look considerably different than they did in the original. The sad part is the original art was better. The original monsters looked more like the summoned hellspawn they were meant to be. These new renditions all look a lot more like your atypical clichéd monsters.
In contrast, the music is nothing but good. The original music was created by famous Final Fantasy composer Nobuo Uematsu. Tsuyoshi Sekito has remastered the original music, and they sound ten times better than the originals. The only thing they shuffled around a bit was the battle music. The original Final Fantasy I lacked boss music completely, and Final Fantasy II's boss music was sparsely used. Both now feature several new battle themes, but don't worry, the originals are in there too. The sound has been remastered too, and there's just no comparison. The 8-bit Nintendo sound effects just can't stand near CD quality sound.