What is the difference between Breath of Fire III for the PSX and for the PSP (or PSPGo)?
AFAIK it's the same with better graphics, picture gallery and the ability to share fishing minigames with friends.
EDIT: Someone made a list of the differences:
The title screen is different
Some slowdown before attacks until you've had the game on for a bit.
The electric room with the machine soldier in the "Factory" has permanent slowdown which actually makes it a lot easier to do that sequence of lever presses. I think this was done on purpose because there's no other parts like it in the game.
Hachio's name is "Haochi"
Heavy Dagger is now more accurately called "Frost Dagger."
The room with the block puzzle in angel tower has one of the passages decreased in width and you can't get into random battles to teleport to the top to skip the puzzle.
Stallion's color scheme is completely different. He is Brown, white, and yellow if I recall.
"Utmost attack" had its name changed to "Vacuum Wave". I think it is because Stallion was supposed to look like "Ultraman", a Japanese hero. Utmost attack must have been one of his techniques?"
In the Desert, getting into random encounters does not turn Ryu in a random direction. Turning right once, then walking straight until you reach Manmo still works thankfully.
Dupe glitch does not work anymore.
The Holy Mantle seems to work better. If you walk perfectly straight, you will go a while without fighting. Take a single turn, and it's battle time though. I remember it doing absolutely nothing.
Finally, all of the music has added instruments which in my opinion make the music in the game a LOT better. I have never heard those extra sounds even on my I-pod. When I play my PSP on TV, you can still hear the new sounds. I wonder if the music had some sort of error in all of the tracks to begin with? Every song I can think of has something new in it.
Source: http://www.gamefaqs.com/boards/196817-breath-of-fire-iii/55291244
In addition to the above changes noted by juan and RedDragon23, BOF3 on the PSP also changed how far in the game is zoomed, resulting in blurry sprites, fonts, and other assets compared to the properly rendered pixel art on the PSX. Just a heads up. Everything else about the game is better, but if your main draw is the wonderful pixel art, you may want to play the original.