It's not surprising that the GBA remake of Final Fantasy V is better than the original. It wasn't a hard task. The original game had arguably the most fully-realized gameplay system of any RPG, easier to understand than Materia and Junctioning, but very detailed. It also had arguably the worst story and script of any Final Fantasy game after 1991. So, in order to be successful, all the game designers had to do was copy the original gameplay without any changes, and provide a readable, competent translation. And that's really all they did.
The new translation is the best one so far, and there have been two already: the fan-made one that has been available on the Internet for years, and the official one used in Final Fantasy Anthology. This time around, the designers opted to follow the lead of the LUNAR games by adding a lot of humour to the script. Unlike the rather bland if competent script for Final Fantasy IV Advance, this one is a lot of fun. Some of the jokes appear so abruptly, with so little apparent purpose, that it seems like the designers inserted them to alleviate their own boredom. For example, I refer to you to the exchange that occurs after you beat the boss called Cray Claw.
And the gameplay remains unchanged, which is exactly the way it should be. The remake adds a few new Jobs and a secret dungeon that you can go through after beating the main story, but these are irrelevant, minor changes. The basic idea is just like it was in 1992, and actually, it stands up pretty well nowadays against the overcomplicated systems devised for new RPGs. Also, like Final Fantasy IV, the remake is considerably faster than the original. For instance, now you can dash anytime you want, and the Thief's Dash ability just makes you dash even faster. This is a very welcome change. A game that focuses primarily on gameplay and learning abilities should be fast-paced. The only problem is that the game sometimes lags, not just in emulators, but even on the GBA itself! If you run into this problem, sorry, you're basically out of luck.
There's really not much more to say. With the new translation and the increased speed, the game is even more fun to play now than when it first came out (provided that you don't encounter the lag). It's better than the original. But again, that's really not such a big achievement.