In the Japanese version of the game, the title screen's text in the Japanese version translates to Mario & Luigi RPG, the Japanese in-game name. Also, the font is slightly more squiggly in the Japanese version.
D-Pad Directions in Mario's House
Extra Battle Points
In the Japanese version of the game, the brothers start out with more Battle Points. Luigi having six more, tallying to sixteen, and Mario having four more, tallying up to fourteen. In the international version, they only start out with ten Battle Points each.
Luigi's "Ya-ho!" sound
In the Japanese version of the game, Luigi makes a grunting noise in the stats screen when the two brothers switch between one-another's viewing of stats. In the International version, it's a "Ya-hoh!" sound.
In the Japanese version, in the Koopa Cruiser when the brothers are about to get their photos taken, the photographer says "Say cheese!" in the Japanese version and "Say Cheep-Cheep" in the international version, making it more Mario-themed.