I was was frustrated with that book, because I felt it did not emphasize the work by Eckert and Mauchly enough with the ENIAC. I attribute this bias due to George Dyson's proximity to the project as a child - his father, Freeman Dyson, has a position at the Institute for Advanced Study in Princeton, and George Dyson was with him during at least some of it.
A book review on Amazon captures a lot of how I felt when reading the book: https://www.amazon.com/gp/customer-reviews/R3R8T7JSHV506U/re...
And some reactions to the New York Review of Books review: http://www.nybooks.com/articles/2012/09/27/who-gets-credit-c...
For further reading, I recommend "ENIAC: The Triumphs and Tragedies of the World's First Computer" by Scott McCartney.