Carry it when
You are moving to a new city today and need your bag on arrival, or you have one manageable suitcase and a reserved seat.
With a Japan Rail Pass, seats with an oversized baggage area are included at no extra cost. Book them by scanning the QR code on your pass at a Shinkansen ticket machine or at any staffed JR desk. Get your Japan Rail Pass
Send it when
You have several large bags, are doing a day trip on the way, or are travelling at peak times. Bags typically arrive the next day.
Pack an overnight bag, since your suitcase will not be with you for a night.