The Japanese game was released twice. The original print comes in a standard "old style" HuCard jewel case. Later it was rereleased with the PC Engine Fan Magazine. This version came in the "new style" HuCard case. The actual games and manuals are 100% identical though, its only the cases that are different. The PCE Fan Edition is probably a bit rarer, but they are both priced the same usually.
The US Magical Chase though has quite a few differences, and is graphically superior to both Japanese versions. I'll let someone else point these out though.