Whether a remake is good depends on whether the changes they made are good or not.
Dragon Quest 3's remake, for instance, fixed the major problems with the original game's stat growth algorithms. In particular, in the original DQ3, using a seed to boost Vitality or Intelligence would actually stunt the character's HP or MP growth (and in the Intelligence case, there was no way to fix that, as Mystic Nuts didn't exist in the original game). In the remake, however, using the seed will cause the character to get the appropriate amount of HP or MP at the next level up.
Dragon Quest 6's remake, however, wasn't so good. For one thing, monster recruitment was removed. Also, they actually made the game balance worse. For instance, there's the Vacuum skill (mistranslated as "Thin Air"). This was a very useful attack that hit all enemies for no cost. In the remake, they made that skill, which was already very useful, *more* powerful. (This incidentally made certain enemies more dangerous than they were originally.) Another example is Magic Burst, whose use was somewhat questionable in the original (spend all your MP to do 3 * MP in damage? Generally not worth it.). In the remake? It now only does MP * 2 in damage, making the ability pretty much pointless. This is especially obnoxious when the character who gets the ability tends to be one of the least useful human characters to begin with.
Incidentally, Dragon Quest 4's remakes make one change that makes balance worse. Healusall/Omniheal cost 36 MP in the original, which felt right (not too cheap to make the game easy, but not the 62 it cost in DQ3). In the remakes? It now costs only 20 MP, which is too little for such a powerful healing spell, especially now that the Hero (who learns the spell) can now equip an item that restores MP as you walk, which she could not in the original.