One distinct similarity between both works is that they seek to retell the narrative of the American nation. Both authors see a fundamental flaw in the historiography of American History. It is in this regard where they are similar. Johnson and Zinn both see a problem in how American History has been related and they seek to change this in their presentations of the historical narrative.
This is about the only similarity between both authors and works. Johnson basks in the glory of the 19th Century, while Zinn feels that the social progressive movements of the 20th Century showed hope and advancement. This starts from a fundamental different starting point. Johnson believes that the narrative of America that embraces economic liberalism and a lack of government intervention represents the very best that America has to offer. For Zinn, the tale of American History is one of power and exploitation. His Marxist read flies in the face of Johnson's embrace of Smith economic and political progression. In this, both works are fundamentally different and thematically incompatible with one another.