According to Osho, the New Man is the exact opposite of the 'superman.' The superman is a refined continuation of the old—stronger, smarter, superior by degrees—still trapped in the same paradigm. The New Man is a radical discontinuity: the old egoic man dies, and a qualitatively different being arises. 'Superman' is a cultural projection born of inferiority; the New Man transcends comparison.
No: a superman is just a better old man, while the new man appears only when the old, ego-based self is dropped.