children education public or private school? (Tokyo)

I am interested in hearing thoughts on pros and cons of Japanese elementary schools; private vs. public.

I am thinking of sending my daughter to Japanese private school from next year but not sure if it is worth the extra costs (juku, entrance fee, etc...) vs. sending her to the local Japanese public school; a school in Setagaya with a decent reputation.

Thoughts, advice much appreciated!!

Thanks,

James