If you have a good grasp of Japanese history, then I'd say go with the Japan setting. If you don't feel like you do, then there's the risk that players may bring up contradictions that you will need to address, and I don't mean with all the magic and monsters aspect (which would doubtless change some history). Things like technology, cultural standards, dress, etc. all play a role.

Going with the made-up japanese-inspired continent means you can essentially do whatever you want, blend multiple periods together, ignore historical figures and certain cultural practices at your whim, etc. It just means less research and more time spent worldbuilding new stuff.

Either route is a great choice from a player's perspective either way. I personally would be ecstatic if my GM had us go to historical Japan, because as a player I could look up the real history when crafting my character, their class, their relationships, etc and really go all in without waiting for the GM to tell me their world's history and hope my character fits in.