If you never played the original, you MISSED OUT. This is absolutely nothing like the rest of the Final Fantasy games, rather it invents its own set of rules, and basically defines what makes a good game. (Read my Review of the Playstation version for the full scoop on that.)
This review will generally just review THIS version of it, what has changed from the original US PSX version, and the good/bad things that come with that.
Good - The core of the gameplay is left perfectly intact. Those that played the original will feel right at home here, as all the classes, weapons, and their individual functions remain 99% unchanged. And on that note, we have been given a couple classes as part of the update; namely the Onion Knight and the Dark Knight. The former is less interesting as an individual class, rather it is a master class much like Gogo from FF VI, and only reveals its true potential at the hands of a character that has mastered every class in the game, at which point it becomes a beast. The Dark Knight, on the other hand, provides a costly, yet effective method of turning Ramza and your generic characters into a special knight class (Like Agrias, Beowulf, etc.). They are very powerful, deadly, and take a long time to become. However, all the work involved in reaching the Dark Knight class proves appropriate, as they are very capable of dealing a lot of damage in a short amount of time.
In addition to the new classes, we are also awarded with a fair amount of new content to go along with the original story and battles. Chiefly among these are a few extra dialogue scenes (Including some movie-like cel-shaded scenes, which even include decent voice-acting in the US version), as well as some extra battle scenes here and there. The former are very nice, and some of which even help tie up some loose ends that the original left wide open, and the latter are more gimmicky, and provide more or less extra things to the game. Still, it's the thought that counts.
Some other, minor, tweaks have been made, such as standardizing Speed and CT timers (Which had some variation in the original Japan vs US version), making Meliadoul's skills effective against non-human targets (Hooray, she doesn't have to collect dust in my party window any more, and is quite powerful), and increasing your party size from 16 to 24 characters. On the other hand, some battles have been made more difficult to be more in line with the original Japanese version, and others have been made easier across the board (The Wiegraf 1 vs 1 fight in Riovanes is the only noticeable example of this.)
Finally we get a very nice amount of multiplayer content, most notably the coop battles that can award some seriously nice equipment, and allow you to acquire some more during the battles through stealing.
First and foremost is the slow-down issue. Having played literally hundreds of hours on the first game, I am VERY aware of it in this game. Those who never played the original or didn't play it much would probably not notice it as much. Basically, every animation in the game, with the exception of a standard weapon hit, has a moderate to serious amount of slow down on the animation. Some are way worse than others, and some are inexplicably good/bad. For instance, Dash/Counter Tackle is SUPER slow. Flare, on the other hand, despite it being a huge animation doesn't receive a lot of slow down. I've poured through dozens of forum posts attempting to explain it, but no matter what the cause, it's there, and there's likely to never be a fix for it. That being said, it's an issue. I didn't find it a game breaking issue by a long shot, but it is there. You can decide on your own what you feel about that.
Another concern among some circles is the changing of the sound quality for the music. Although I'm a band director, composer, etc. myself, I've got to say that I think this complaint is a little shortsighted. I'd estimate that 90-95% of the game's sounds are intact from the PSX version, and the ones that have been changed aren't anywhere close to the "laughable quality" that I've heard some naysayers hyping about. Is it comparable to an ultra-high quality recording? No. But neither is the PSX version.
The script, dialogue, class, and skill names have all received a re-translation. The class and skill names are now closer to the other final fantasy games, and the japanense version, i.e. Lancer = Dragoon, Fire 4 = Firaja. This comes as a bit of an annoyance to those of us who are very used to the original names; I prefer "sleep" to "repose". The script is a little more bothersome, especially when you're first getting into it. Some people claim it's an improvement, whereas I think the original was fine how it is. Basically they rewrote the whole thing in an "Old English" sort of translation, lots of "sires", and whatnot. It's not bad once you get into it, but very unnecessary if you ask me. Also, whether it's closer to the original *** translation or not, some liberties were taken with some of the meanings of the dialogue, changing some conversations and characters to a not inconsiderable degree.
Unfortunately, along with some of the good minor tweaks came some bad ones. One of the ones that annoyed me the most was the fact that, in accordance with the original Japanese version, you can no longer steal the Genji Armor from Marquis Elmdor :/ This, I think, is a very bad call on their part, as this was a very big challenge in the original. You basically had to gimp yourself, be patient, and fight the battle in a very unique way in order to both steal his armor, and win the battle. Instead, on my run-through of this, the battle ended in a single turn. Very sad.
The multi-player, while absolutely cool, is very stunted by the fact that it is LAN only. That means you better know someone with a PSP and this game in a driving range if you plan on experiencing all the great multi-player features.
All in all, I enjoyed playing through this again, and if you've never experienced it and have a PSP, I would highly recommend picking this up, especially considering the game itself is now like 5 dollars on Amazon.com. Have fun.