Art is currently from the European manual and the Super Bomberman Complete Encyclopedia guidebook. Artwork hasn't been cleaned up, so expect bits of book border and whatnot.
The English release adds a trademark symbol, updates the copyright details and brightens up the font.
Waiting on the title screen of the Japanese version will play a demo, alternating between battle mode demos and a slideshow of game's story (as basic as it is). This was dropped from the English version and only battle demos are shown. No idea why - it's not like there's any text to translate.
The Moguchan enemies from World 3 had their appearance changed between the Japanese and English releases. The Japanese versions are brown and red with big grinning mouths, while their Western counterparts are green and purple, and have no mouths at all. Given the unfortunate resemblance to blackface makeup, it's a pretty reasonable change. Although the sprites were modified, Moguchan's artwork appears untouched in the English manual.
The bosses of world 5 have unique colours in the Japanese version, but merely share Bomberman's palette in the English release.
Likewise, the Bombermen at the end have odd palettes (yellow faces, white arms, red/orange appendages), even though in battle mode they still appear with their usual skin tones in both versions.
The yellow faces and red appendages also show up in the Battle Mode victory artwork. The English version restores their usual caucasian tones and pink bits.
The Japanese "Draw" screen features the player Bombermen tumbling on-screen in a defeated heap. The English version instead has the "Draw" letters drop on-screen, and the Bombermen don't appear at all.