I'll probably give it a pass since game remakes to me are pointless, but maybe people will dig it.
How good a remake depends. Some are excellent (Dragon Quest 3. which fixed some of the game's ugly mechanics (particularly HP/MP growth) and added a lot of new stuff), while some not so much (like Dragon Quest 6, which removed monster recruitment and made game balance worse, or the WonderSwan Color version of FF2, which slowed down magic leveling, and which the PSX version is based on).
Final Fantasy 3's remake has both good and bad points. For example:
+: Bards are useful in this version. (They weren't in the original.)
+: Some other nice job re-works, like the Dark Knight getting Souleater but losing white magic, or the Warrior getting Advance for extra damage at the cost of defense. Also means that early jobs no longer become obsolete (I've used both Warrior and Red Mage in the endgame, and they are definitely useful).
+: The music remixes are well done (even if the trumpets in a couple tracks are not pleasant to listen to, and there's a couple tracks that lost something that was in the original, like an extra voice or octave shift).
-: Fewer enemies per battle.
-: Status ailments almost never work. (In the original, they worked almost always, unless targeted on the enemy during a boss fight. (Yes, there's an explicit boss check in FF3, probably a reaction to FF2 bosses )
-: In the first iteration of the remake (the DS version), there's single player content locked behind multiplayer, where the multiplayer just consists of the ability to send 1 message to a friend per hour. Fortunately, later versions (like the PSP version) changed this. (Note that you can no longer send mognet messages over the internet through official means.)
?: The remake is actually *harder* than the original. Also, they did not fix the issue of the final dungeon being too long after the one place you can save.