I can't really decide whether I enjoyed 3 or 4 more, but both were disappointements after part 2.
Breath of Fire 3 is a decent rpg with decent mechanics, a decent story that ties closely into Breath of Fire 1, and a decent, but mostly boring cast (save Rei and Momo). It also has a crybaby Ryu and an annoying, mentally challenged Nina who lacked the depth of the Ninas from 2 and 4 but had not a whit of the charm of the first Nina. Also, Deis (Bleu) is not playable, unlike 1,2, and 4. I wish I could have played as Teepo in Ryu's place.
Part 4 streamlined the mechanics and improved on the story and graphics, but much of the game was recycled from 3. Sprites were much larger and had fantastic animation. The towns were large and complex with tall structures and cool focus effects. The main dragon transformation was pretty cool and Fou Lu was awesomefor most of the game. The story was fairly original for a JRPG, but the ending seemed to set up for a sequel and left much unresolved. My main issued was that part 3 was easy, but part 4 had no challenge at all...ever.
Breath of Fire 2 and 5 are the only games in the series I consider worth owning, although 2 has been aped by many games since and has not really aged all that well. At the time it was something very special.
Still, those graphics sure look pretty.