Rent is cheaper but certainly not cheap but for about HK 20,000- 30,000 you get more space (say 700 to 900 square feet or so). I would say, on average, commuting times may be longer, Tokyo being so much larger than HK. Food is more expensive as is eating out but food is higher quality- so if you were buying imported Japanese fruit and vegetables and organic and such, well Japan will be cheaper. But if you were just buying local stuff then food will be more expensive. Obviously a huge variable here depending on your tastes and how much meat and such you choose to eat.
I think I also paid more in utilities as you need heat in the winter and AC in the summer. It's not really one thing, more of an overall combination of things that may make things like food and utilities and such more expensive.
I think school is (or used to be) easier to get into and no debentures but was still not cheap- for my daughter, the first year of high school was about 160,000 HKD back in 2003...so I don't imagine you will see huge tuition savings.