I like the way FireRed and LeafGreen portray the original Red and Blue. It is nearly the same until the 8th Gym where the Sevii Islands became part of the story. The Sevii Islands, however were a welcome addition to the games. The Sevii Islands give a bit more Post-game content instead of going straight to Mewtwo and allow entry for some Non-Kanto Pokemon.
HeartGold and SoulSilver take remakes to the next level. The introduction of Lyra makes things a bit different. Also the opposite PC has a bigger role in the story. They added a Safari Zone which was not present in the originals. They even have Walking Pokemon, which makes Pokemon feel a bit more realistic. Then, there is a fan service in the form of the GB sounds. That makes the remakes superior to the originals in my opinion.
Overall I think Game Freak does a good job with remakes.